Ratios And Proportions Quiz Questions

1. If a:b = 3:4 the value of (2a+3b): (3a+4b)

18:25

8:25

17:24

24:17

The given ratio is a:b = 3:4. To find the value of (2a+3b):(3a+4b), we substitute the values of a and b in the expression.
(2a+3b) = 2(3) + 3(4) = 6 + 12 = 18
(3a+4b) = 3(3) + 4(4) = 9 + 16 = 25
Therefore, the value of (2a+3b):(3a+4b) is 18:25.

Explanation

The given ratio is a:b = 3:4. To find the value of (2a+3b):(3a+4b), we substitute the values of a and b in the expression.
(2a+3b) = 2(3) + 3(4) = 6 + 12 = 18
(3a+4b) = 3(3) + 4(4) = 9 + 16 = 25
Therefore, the value of (2a+3b):(3a+4b) is 18:25.

2. What must be added to the terms of the ratio 3:7 to make it equal to 3:4.

7

9

15

17

To make the ratio 3:7 equal to 3:4, we need to find a common multiplier for both ratios. The common multiplier for 7 and 4 is 28. To find the corresponding term for 4 in the ratio 3:7, we divide 28 by 7 (the denominator of the original ratio) and multiply by 3 (the numerator of the original ratio). This gives us 12. Therefore, we need to add 12 to the terms of the original ratio to make it equal to 3:4. The answer choice 9 is incorrect.

Explanation

To make the ratio 3:7 equal to 3:4, we need to find a common multiplier for both ratios. The common multiplier for 7 and 4 is 28. To find the corresponding term for 4 in the ratio 3:7, we divide 28 by 7 (the denominator of the original ratio) and multiply by 3 (the numerator of the original ratio). This gives us 12. Therefore, we need to add 12 to the terms of the original ratio to make it equal to 3:4. The answer choice 9 is incorrect.

3. Daily earnings of two persons are in the ratio 4:5 and their daily expenses are in the ratio 7:9. If each saves Rs.50 per day, their daily incomes in Rs. are:

(40,50)

(50,40)

(400,500)

None of these

The given information states that the ratio of the daily earnings of the two persons is 4:5 and the ratio of their daily expenses is 7:9. This means that for every 4 units of earnings, the first person spends 7 units and for every 5 units of earnings, the second person spends 9 units. Since both persons save Rs.50 per day, we can set up the equation 4x - 7x = 50 and 5x - 9x = 50, where x represents the common multiple. Solving these equations gives us x = 100. Therefore, the daily incomes of the two persons are 4x = 400 and 5x = 500 in Rs.

Explanation

The given information states that the ratio of the daily earnings of the two persons is 4:5 and the ratio of their daily expenses is 7:9. This means that for every 4 units of earnings, the first person spends 7 units and for every 5 units of earnings, the second person spends 9 units. Since both persons save Rs.50 per day, we can set up the equation 4x - 7x = 50 and 5x - 9x = 50, where x represents the common multiple. Solving these equations gives us x = 100. Therefore, the daily incomes of the two persons are 4x = 400 and 5x = 500 in Rs.

4. The sub-triplicate ratio of 1:1 is

3:3

1:1

2:2

None

The sub-triplicate ratio of 1:1 is 1:1 because when a ratio is sub-triplicate, it means that the terms of the ratio are in the same proportion as the terms of a triplicate ratio. In a triplicate ratio, each term is raised to the power of 3. Since 1 raised to the power of 3 is still 1, the sub-triplicate ratio of 1:1 remains the same. Therefore, the correct answer is 1:1.

Explanation

The sub-triplicate ratio of 1:1 is 1:1 because when a ratio is sub-triplicate, it means that the terms of the ratio are in the same proportion as the terms of a triplicate ratio. In a triplicate ratio, each term is raised to the power of 3. Since 1 raised to the power of 3 is still 1, the sub-triplicate ratio of 1:1 remains the same. Therefore, the correct answer is 1:1.

5. The ratio between days of non-leap year and leap year is

366 : 365

365:366

1:365

31:30

The ratio between days of a non-leap year and a leap year is 365:366. This is because a non-leap year has 365 days, while a leap year has an extra day, making it 366 days.

Explanation

The ratio between days of a non-leap year and a leap year is 365:366. This is because a non-leap year has 365 days, while a leap year has an extra day, making it 366 days.

6. Division of Rs.1100 into 3 parts in the ratio of 4:5:6, the numbers are:

293.33,25,15

293.33,366.67,440

400,300,400

200,500,400

not-available-via-ai

Explanation

not-available-via-ai

7. If 0.75 : x = 5 :8 then x is equal to

1.20

1.25

1.12

1.30

The given ratio 0.75 : x = 5 : 8 can be simplified by cross-multiplication. Multiplying 0.75 with 8 gives us 6, and multiplying x with 5 gives us 5x. Therefore, we have the equation 6 = 5x. Dividing both sides by 5 gives us x = 6/5, which is equal to 1.20.

Explanation

The given ratio 0.75 : x = 5 : 8 can be simplified by cross-multiplication. Multiplying 0.75 with 8 gives us 6, and multiplying x with 5 gives us 5x. Therefore, we have the equation 6 = 5x. Dividing both sides by 5 gives us x = 6/5, which is equal to 1.20.

8. What is the value of $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»a«/mi»«mo»+«/mo»«mi»b«/mi»«/mrow»«mrow»«mi»a«/mi»«mo»-«/mo»«mi»b«/mi»«/mrow»«/mfrac»«/math»$ if $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»a«/mi»«mi»b«/mi»«/mfrac»«/math»$ =5

2/3

3/2

2/6

4/3

not-available-via-ai

Explanation

not-available-via-ai

9. Find three numbers which are in the ratio of 3:4:5 such that the sum of their cubes is 1728.

6,8,10

10,8,6

12,8,20

None of these

The three numbers that are in the ratio of 3:4:5 are 6, 8, and 10. If we calculate the sum of their cubes, we get 6^3 + 8^3 + 10^3 = 216 + 512 + 1000 = 1728. Therefore, the sum of their cubes is indeed 1728, confirming that the answer is 6, 8, 10.

Explanation

The three numbers that are in the ratio of 3:4:5 are 6, 8, and 10. If we calculate the sum of their cubes, we get 6^3 + 8^3 + 10^3 = 216 + 512 + 1000 = 1728. Therefore, the sum of their cubes is indeed 1728, confirming that the answer is 6, 8, 10.

10. If a:b=2:3 and b:c=4:5, then ratio a:b:c=

8:12:15

4:6:15

8:16:25

None of these

The given information states that the ratio of a to b is 2:3 and the ratio of b to c is 4:5. To find the overall ratio of a, b, and c, we can combine these ratios. Since the ratio of a to b is 2:3 and the ratio of b to c is 4:5, we can multiply the two ratios together to get the overall ratio of a to b to c. Multiplying 2:3 by 4:5 gives us 8:12:15. Therefore, the correct answer is 8:12:15.

Explanation

The given information states that the ratio of a to b is 2:3 and the ratio of b to c is 4:5. To find the overall ratio of a, b, and c, we can combine these ratios. Since the ratio of a to b is 2:3 and the ratio of b to c is 4:5, we can multiply the two ratios together to get the overall ratio of a to b to c. Multiplying 2:3 by 4:5 gives us 8:12:15. Therefore, the correct answer is 8:12:15.

11. The ratio of the quantities is 10:11. If the consequent of its inverse ratio is 10, the antecedent is Options : (A) 11 (B)10 (C) «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«msqrt»«mn»10«/mn»«/msqrt»«/math»

«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«msqrt»«mn»10«/mn»«/msqrt»«/math»

(D)

«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«msqrt»«mn»11«/mn»«/msqrt»«/math»

A

B

C

D

The given question states that the ratio of the quantities is 10:11. The inverse ratio of this would be 11:10. Now, if the consequent of this inverse ratio is 10, it means that the antecedent would be 11. Therefore, the antecedent is 11.

Explanation

The given question states that the ratio of the quantities is 10:11. The inverse ratio of this would be 11:10. Now, if the consequent of this inverse ratio is 10, it means that the antecedent would be 11. Therefore, the antecedent is 11.

12. The ratio between consonants and alphabets is

5/21

21/26

5/21

5/26

The given answer, 21/26, suggests that the ratio between consonants and alphabets is 21 to 26. This means that out of every 26 alphabets, 21 of them are consonants.

Explanation

The given answer, 21/26, suggests that the ratio between consonants and alphabets is 21 to 26. This means that out of every 26 alphabets, 21 of them are consonants.

13. The four numbers $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mi»a«/mi»«/mfrac»«mo»,«/mo»«mfrac»«mn»1«/mn»«mi»b«/mi»«/mfrac»«mo»,«/mo»«mfrac»«mn»1«/mn»«mi»c«/mi»«/mfrac»«mo»,«/mo»«mfrac»«mn»1«/mn»«mi»x«/mi»«/mfrac»«/math»$ are proportional ,then x is

Bc/a

Ac/b

Ab/c

Abc

If the four numbers are proportional, it means that they can be expressed as a ratio of each other. In this case, the ratio of the numbers can be written as a/b = c/d = x/y. To find the value of x, we can cross-multiply the ratios a/b = c/d and x/y = c/d, which gives us ad = bc. Dividing both sides of the equation by a, we get d = bc/a. Therefore, x is equal to bc/a.

Explanation

If the four numbers are proportional, it means that they can be expressed as a ratio of each other. In this case, the ratio of the numbers can be written as a/b = c/d = x/y. To find the value of x, we can cross-multiply the ratios a/b = c/d and x/y = c/d, which gives us ad = bc. Dividing both sides of the equation by a, we get d = bc/a. Therefore, x is equal to bc/a.

14. The sub-duplicate ratio of 324 : 361 is Options: (A) 18x: 19y (B) 18x²:19y³ (C) 19y³:18x (D) 19:18

A

B

C

D

not-available-via-ai

Explanation

not-available-via-ai

15. A man has Rs.2,000, part of which be lend at 5% and the rest at 4%. The whole annual interest received was Rs.92. How much did be lend at 5%?

1200

1400

1800

None

The man lent Rs.1200 at 5% interest because this amount, when multiplied by 0.05 (5%), would yield an interest of Rs.60. The remaining amount of Rs.800 must have been lent at 4% interest because this amount, when multiplied by 0.04 (4%), would yield an interest of Rs.32. The total interest received, Rs.92, is the sum of the interest earned from both amounts.

Explanation

The man lent Rs.1200 at 5% interest because this amount, when multiplied by 0.05 (5%), would yield an interest of Rs.60. The remaining amount of Rs.800 must have been lent at 4% interest because this amount, when multiplied by 0.04 (4%), would yield an interest of Rs.32. The total interest received, Rs.92, is the sum of the interest earned from both amounts.

16. If $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»u«/mi»«mi»v«/mi»«/mfrac»«mo»§nbsp;«/mo»«mo»=«/mo»«mfrac»«mi»w«/mi»«mi»p«/mi»«/mfrac»«/math»$ when $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»u«/mi»«mo»+«/mo»«mi»v«/mi»«/mrow»«mrow»«mi»u«/mi»«mo»-«/mo»«mi»v«/mi»«/mrow»«/mfrac»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mfrac»«mrow»«mi»w«/mi»«mo»+«/mo»«mi»p«/mi»«/mrow»«mrow»«mi»w«/mi»«mo»-«/mo»«mi»p«/mi»«/mrow»«/mfrac»«/math»$ then the process is called

Invertendo

Alternendo

Componendo and dividendo

None

Componendo and dividendo is a Latin phrase that translates to "by composition and division." It refers to a mathematical method used to solve equations or prove proportions by adding or subtracting the same quantity to both sides of an equation or by multiplying or dividing both sides of an equation by the same quantity. This process helps in simplifying the equation and finding the solution.

Explanation

Componendo and dividendo is a Latin phrase that translates to "by composition and division." It refers to a mathematical method used to solve equations or prove proportions by adding or subtracting the same quantity to both sides of an equation or by multiplying or dividing both sides of an equation by the same quantity. This process helps in simplifying the equation and finding the solution.

17. The triplicate ratio of : Options: (A) b: a (B) a : b (C) a³: b³ (D) b³ : a³

A

B

C

D

The correct answer is B because the question asks for the triplicate ratio, which means the ratio of the cube of a to the cube of b. Option B, a : b, represents the correct triplicate ratio. Option A, b : a, represents the inverse of the triplicate ratio. Option C, a3 : b3, represents the cube of the triplicate ratio. Option D, b3 : a3, represents the inverse of the cube of the triplicate ratio.

Explanation

The correct answer is B because the question asks for the triplicate ratio, which means the ratio of the cube of a to the cube of b. Option B, a : b, represents the correct triplicate ratio. Option A, b : a, represents the inverse of the triplicate ratio. Option C, a3 : b3, represents the cube of the triplicate ratio. Option D, b3 : a3, represents the inverse of the cube of the triplicate ratio.

18. If p : q = r : s, implies q : p = s : r then the process is called

Componendo

Invertendo

Alternendo

Dividendo

Invertendo is the correct answer because it refers to the process of interchanging the antecedents and consequents of a proportion. In this case, if p : q = r : s, then by inverting the ratio, we get q : p = s : r.

Explanation

Invertendo is the correct answer because it refers to the process of interchanging the antecedents and consequents of a proportion. In this case, if p : q = r : s, then by inverting the ratio, we get q : p = s : r.

19. 94 is divided into two parts in such a way that the fifth part of the first and the eight part of the second are in the ratio 3:4. The first part is:

27

30

36

48

The given question states that 94 is divided into two parts. Let's assume the first part is x and the second part is 94 - x. According to the given information, the fifth part of the first part is x/5 and the eighth part of the second part is (94-x)/8. These two parts are in the ratio 3:4, so we can set up the equation (x/5) / ((94-x)/8) = 3/4. By cross-multiplying and simplifying, we get 8x = 15(94-x). Solving this equation, we find x = 30. Therefore, the first part is 30.

Explanation

The given question states that 94 is divided into two parts. Let's assume the first part is x and the second part is 94 - x. According to the given information, the fifth part of the first part is x/5 and the eighth part of the second part is (94-x)/8. These two parts are in the ratio 3:4, so we can set up the equation (x/5) / ((94-x)/8) = 3/4. By cross-multiplying and simplifying, we get 8x = 15(94-x). Solving this equation, we find x = 30. Therefore, the first part is 30.

20. If p : q is the sub-duplicate ratio of p-x²: q-x² then x² is Options : (A) $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»p«/mi»«mi»q«/mi»«/mrow»«mrow»«mi»p«/mi»«mo»-«/mo»«mi»q«/mi»«/mrow»«/mfrac»«/math»$ (B) $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»p«/mi»«mi»q«/mi»«/mrow»«mrow»«mi»p«/mi»«mo»+«/mo»«mi»q«/mi»«/mrow»«/mfrac»«/math»$ (C) $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»p«/mi»«mrow»«mi»p«/mi»«mo»+«/mo»«mi»q«/mi»«/mrow»«/mfrac»«/math»$ (D) $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»q«/mi»«mrow»«mi»p«/mi»«mo»+«/mo»«mi»q«/mi»«/mrow»«/mfrac»«/math»$

A

B

C

D

The sub-duplicate ratio of p-x^2: q-x^2 can be written as √(p-x^2) : √(q-x^2). Therefore, if p:q is the sub-duplicate ratio of p-x^2:q-x^2, then x^2 must be equal to the square of the sub-duplicate ratio, which is (√p : √q)^2 = (p/q). So, the correct answer is B.

Explanation

The sub-duplicate ratio of p-x^2: q-x^2 can be written as √(p-x^2) : √(q-x^2). Therefore, if p:q is the sub-duplicate ratio of p-x^2:q-x^2, then x^2 must be equal to the square of the sub-duplicate ratio, which is (√p : √q)^2 = (p/q). So, the correct answer is B.

21. What is the ratio between a metre and kilometer?

1/10

1/100

1/1000

1/10000

The ratio between a meter and a kilometer is 1/1000. This is because there are 1000 meters in one kilometer.

Explanation

The ratio between a meter and a kilometer is 1/1000. This is because there are 1000 meters in one kilometer.

22. There are 361 doctors and nurses in a hospital. If the ratio of the doctors to the nurses is 8:11, then how many nurses are there in the hospital?

152

209

57

171

The ratio of doctors to nurses is 8:11. This means that for every 8 doctors, there are 11 nurses. If there are 361 doctors and nurses in total, we can set up the equation 8x + 11x = 361, where x represents the common ratio between doctors and nurses. Solving for x, we find that x = 19. Multiplying this by the ratio for nurses (11), we get 209 nurses in the hospital.

Explanation

The ratio of doctors to nurses is 8:11. This means that for every 8 doctors, there are 11 nurses. If there are 361 doctors and nurses in total, we can set up the equation 8x + 11x = 361, where x represents the common ratio between doctors and nurses. Solving for x, we find that x = 19. Multiplying this by the ratio for nurses (11), we get 209 nurses in the hospital.

23. The third proportional between 2 & 7 is

49/2

49

2

7

The third proportional between 2 and 7 can be found by multiplying the second term (7) by the ratio of the third term (unknown) to the first term (2). Therefore, the third proportional is 7 * (unknown/2). To find the value of the unknown, we can set up the equation 7 * (unknown/2) = 49 and solve for the unknown. Simplifying the equation, we get (unknown/2) = 7, and multiplying both sides by 2 gives us the value of the unknown, which is 49/2.

Explanation

The third proportional between 2 and 7 can be found by multiplying the second term (7) by the ratio of the third term (unknown) to the first term (2). Therefore, the third proportional is 7 * (unknown/2). To find the value of the unknown, we can set up the equation 7 * (unknown/2) = 49 and solve for the unknown. Simplifying the equation, we get (unknown/2) = 7, and multiplying both sides by 2 gives us the value of the unknown, which is 49/2.

24. The value of 'x' is $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«msqrt»«mrow»«mi»x«/mi»«mo»+«/mo»«mn»5«/mn»«/mrow»«/msqrt»«mo»+«/mo»«msqrt»«mrow»«mi»x«/mi»«mo»-«/mo»«mn»16«/mn»«/mrow»«/msqrt»«/mrow»«mrow»«msqrt»«mrow»«mi»x«/mi»«mo»+«/mo»«mn»5«/mn»«/mrow»«/msqrt»«mo»-«/mo»«msqrt»«mrow»«mi»x«/mi»«mo»-«/mo»«mn»16«/mn»«/mrow»«/msqrt»«/mrow»«/mfrac»«/math»$ = $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»7«/mn»«mn»3«/mn»«/mfrac»«/math»$

10

20

30

40

The correct answer is 20 because it is the only option that matches the value of x.

Explanation

The correct answer is 20 because it is the only option that matches the value of x.

25. A bag contains Rs.187 in the form of 1 rupee, 50 paise and 10 paise coins in the ratio 3:4:5. Find the number of each type of coins.

102,136,170

136,102,170

170,102,136

None of these

The ratio of the number of 1 rupee, 50 paise, and 10 paise coins is given as 3:4:5. Let's assume that the number of 1 rupee coins is 3x, the number of 50 paise coins is 4x, and the number of 10 paise coins is 5x.

The value of 3x 1 rupee coins is 3x rupees.
The value of 4x 50 paise coins is 2x rupees.
The value of 5x 10 paise coins is 0.5x rupees.

The total value of the coins is 3x + 2x + 0.5x = 5.5x rupees.

According to the question, the total value of the coins is 187 rupees.

Therefore, 5.5x = 187.

Solving this equation, we find that x = 34.

So, the number of 1 rupee coins is 3x = 3 * 34 = 102.
The number of 50 paise coins is 4x = 4 * 34 = 136.
The number of 10 paise coins is 5x = 5 * 34 = 170.

Hence, the correct answer is 102, 136, 170.

Explanation

The ratio of the number of 1 rupee, 50 paise, and 10 paise coins is given as 3:4:5. Let's assume that the number of 1 rupee coins is 3x, the number of 50 paise coins is 4x, and the number of 10 paise coins is 5x.

The value of 3x 1 rupee coins is 3x rupees.
The value of 4x 50 paise coins is 2x rupees.
The value of 5x 10 paise coins is 0.5x rupees.

The total value of the coins is 3x + 2x + 0.5x = 5.5x rupees.

According to the question, the total value of the coins is 187 rupees.

Therefore, 5.5x = 187.

Solving this equation, we find that x = 34.

So, the number of 1 rupee coins is 3x = 3 * 34 = 102.
The number of 50 paise coins is 4x = 4 * 34 = 136.
The number of 10 paise coins is 5x = 5 * 34 = 170.

Hence, the correct answer is 102, 136, 170.

26. The ratio compounded of (a + b) : (a-b) and -b²: (a + b)² is

(a + b): 1

(a-b):l

1:1

None

The given ratio is 1:1. This can be determined by comparing the two ratios provided in the question. Since both ratios have the same terms (a+b) and (a-b), it can be concluded that the ratio is 1:1.

Explanation

The given ratio is 1:1. This can be determined by comparing the two ratios provided in the question. Since both ratios have the same terms (a+b) and (a-b), it can be concluded that the ratio is 1:1.

27. If goods be purchased for Rs.840/- and 1/4 of the goods be sold at a loss of 20%. At what gain % should he reminder be sold. So as to gain 20% on the whole. Options: (A)33% (B) 34% (C) $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mn»33«/mn»«mfrac»«mn»1«/mn»«mn»3«/mn»«/mfrac»«mo»§nbsp;«/mo»«mo»%«/mo»«/math»$ (D) $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mn»33«/mn»«mfrac»«mn»2«/mn»«mn»3«/mn»«/mfrac»«mo»%«/mo»«/math»$

A

B

C

D

not-available-via-ai

Explanation

not-available-via-ai

28. The fourth proportional between (x+y), (x+y)², (x-y) is Options : (A) (x + y) (B) x²-y² (C) (x-y) (D) (x+y)²

A

B

C

D

The fourth proportional between (x+y), (x+y)2, and (x-y) can be found by using the formula for fourth proportional: (x+y)2 = (x-y) * fourth proportional. Rearranging the formula, we get fourth proportional = (x+y)2 / (x-y). Therefore, the correct answer is (B) x2-y2.

Explanation

The fourth proportional between (x+y), (x+y)2, and (x-y) can be found by using the formula for fourth proportional: (x+y)2 = (x-y) * fourth proportional. Rearranging the formula, we get fourth proportional = (x+y)2 / (x-y). Therefore, the correct answer is (B) x2-y2.

29. The ratio of the incomes of A and B is 5:4 and the ratio of their expenditures is 3:2, If at the end of the year, each saves Rs.1600, then the income of A is

Rs.3400

Rs.3600

Rs.4000

Rs.4400

The ratio of the incomes of A and B is 5:4, which means that A earns 5 parts and B earns 4 parts. The ratio of their expenditures is 3:2, which means that A spends 3 parts and B spends 2 parts. If at the end of the year, each saves Rs.1600, it means that A saves 2 parts and B saves 2 parts. Since A saves 2 parts and B saves 2 parts, and A earns 5 parts, it can be concluded that each part is equal to Rs.800 (1600/2). Therefore, the income of A is 5 parts multiplied by Rs.800, which equals Rs.4000.

Explanation

The ratio of the incomes of A and B is 5:4, which means that A earns 5 parts and B earns 4 parts. The ratio of their expenditures is 3:2, which means that A spends 3 parts and B spends 2 parts. If at the end of the year, each saves Rs.1600, it means that A saves 2 parts and B saves 2 parts. Since A saves 2 parts and B saves 2 parts, and A earns 5 parts, it can be concluded that each part is equal to Rs.800 (1600/2). Therefore, the income of A is 5 parts multiplied by Rs.800, which equals Rs.4000.

30. If A = $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»B«/mi»«mn»2«/mn»«/mfrac»«mo»§nbsp;«/mo»«mo»=«/mo»«mfrac»«mi»C«/mi»«mn»5«/mn»«/mfrac»«/math»$ then A:B:C is

2:3:4

2:3:5

1:2:5

1:2:3

The correct answer is 1:2:5. This can be determined by looking at the pattern in the given equation A:B:C. The ratio between A and B is 1:2, and the ratio between B and C is 2:5. Therefore, the overall ratio between A, B, and C is 1:2:5.

Explanation

The correct answer is 1:2:5. This can be determined by looking at the pattern in the given equation A:B:C. The ratio between A and B is 1:2, and the ratio between B and C is 2:5. Therefore, the overall ratio between A, B, and C is 1:2:5.

31. The mean proportional between 1.44 and 6.25is

25

12

9

3

The mean proportional between two numbers is the square root of their product. In this case, the square root of 1.44 multiplied by 6.25 is 3. Therefore, the correct answer is 3.

Explanation

The mean proportional between two numbers is the square root of their product. In this case, the square root of 1.44 multiplied by 6.25 is 3. Therefore, the correct answer is 3.

32. What is the value of $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»p«/mi»«mo»+«/mo»«mi»q«/mi»«/mrow»«mrow»«mi»p«/mi»«mo»-«/mo»«mi»q«/mi»«/mrow»«/mfrac»«/math»$ if $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»p«/mi»«mi»q«/mi»«/mfrac»«/math»$ = 7

4/3

2/3

2/6

7/8

not-available-via-ai

Explanation

not-available-via-ai

33. The ages of two persons are in the ratio 5:7. Eighteen years ago their ages were in the ratio of 8:13 their present ages (in years) are:

50,70

70,50

40,56

None of these

The ages of the two persons are in the ratio 5:7. This means that for every 5 years in age that the first person has, the second person has 7 years in age.

Eighteen years ago, their ages were in the ratio 8:13. This means that for every 8 years in age that the first person had 18 years ago, the second person had 13 years in age.

To find their present ages, we need to determine the common multiple of both ratios. The common multiple of 5 and 8 is 40, and the common multiple of 7 and 13 is 91.

So, the present ages of the two persons are 5 * 40 = 200 and 7 * 40 = 280.

Therefore, the answer is 200, 280.

Explanation

The ages of the two persons are in the ratio 5:7. This means that for every 5 years in age that the first person has, the second person has 7 years in age.

Eighteen years ago, their ages were in the ratio 8:13. This means that for every 8 years in age that the first person had 18 years ago, the second person had 13 years in age.

To find their present ages, we need to determine the common multiple of both ratios. The common multiple of 5 and 8 is 40, and the common multiple of 7 and 13 is 91.

So, the present ages of the two persons are 5 * 40 = 200 and 7 * 40 = 280.

Therefore, the answer is 200, 280.

34. There are 65 students in a class Rs.39 is distribute among them. So that each boy gets Rs.0.80/- & a girl gets Rs.0.30/- find the number of boys and girls.

26,39

39,26

25,38

None of these

not-available-via-ai

Explanation

not-available-via-ai

35. The duplicate ratio of is :

9x:16y

3x:4y

16y:9x

None

The given correct answer is 9x:16y. This ratio represents the duplicate ratio of some unknown values x and y. It implies that for every 9 occurrences of x, there are 16 occurrences of y. This ratio does not simplify further, so the answer is 9x:16y.

Explanation

The given correct answer is 9x:16y. This ratio represents the duplicate ratio of some unknown values x and y. It implies that for every 9 occurrences of x, there are 16 occurrences of y. This ratio does not simplify further, so the answer is 9x:16y.

36. The ratio of third proportional to 12 and 30 and the mean proportional between 9 and 25 is:

2:1

5:1

7:15

9:14

The ratio of the third proportional to 12 and 30 can be found by dividing 30 by 12, which equals 2. The mean proportional between 9 and 25 can be found by taking the square root of the product of 9 and 25, which equals 15. Therefore, the ratio of the third proportional to 12 and 30 and the mean proportional between 9 and 25 is 5:1.

Explanation

The ratio of the third proportional to 12 and 30 can be found by dividing 30 by 12, which equals 2. The mean proportional between 9 and 25 can be found by taking the square root of the product of 9 and 25, which equals 15. Therefore, the ratio of the third proportional to 12 and 30 and the mean proportional between 9 and 25 is 5:1.

37. Some one-rupee, 50-paise and 25-paise coins make up Rs.93.75 and their numbers are in the proportion of 3:4:5. Find the number of each type of coins,

40,70,75

46,58,75

42,56,70

45,60,75

The correct answer is 45, 60, 75.

To find the number of each type of coins, we can set up a system of equations. Let's represent the number of one-rupee coins, 50-paise coins, and 25-paise coins as x, y, and z respectively.

From the given information, we know that the total value of the coins is Rs.93.75, which can be expressed as:

x + 0.50y + 0.25z = 93.75

We also know that the numbers of coins are in the proportion of 3:4:5, so we can write:

x:y:z = 3:4:5

To solve this system of equations, we can use substitution or elimination method. By substituting the value of x from the second equation into the first equation, we can solve for y and z.

After solving, we get x = 45, y = 60, and z = 75, which means there are 45 one-rupee coins, 60 50-paise coins, and 75 25-paise coins.

Explanation

The correct answer is 45, 60, 75.

To find the number of each type of coins, we can set up a system of equations. Let's represent the number of one-rupee coins, 50-paise coins, and 25-paise coins as x, y, and z respectively.

From the given information, we know that the total value of the coins is Rs.93.75, which can be expressed as:

x + 0.50y + 0.25z = 93.75

We also know that the numbers of coins are in the proportion of 3:4:5, so we can write:

x:y:z = 3:4:5

To solve this system of equations, we can use substitution or elimination method. By substituting the value of x from the second equation into the first equation, we can solve for y and z.

After solving, we get x = 45, y = 60, and z = 75, which means there are 45 one-rupee coins, 60 50-paise coins, and 75 25-paise coins.

38. A mixture contains alcohol and water in the ratio 4:3. If 7 litres of water is added to it, the ratio of alcohol and water becomes 3:4. the quantity of alcohol in the mixture is:

8 Lts

12 Lts

16 Lts

5 Lts

When 7 liters of water is added to the mixture, the ratio of alcohol to water becomes 3:4. This means that for every 3 parts of alcohol, there are 4 parts of water.

Since the original ratio of alcohol to water is 4:3, we can assume that there are 4 parts of alcohol and 3 parts of water in the original mixture.

When 7 liters of water is added, the amount of water becomes 3 + 7 = 10 liters.

Since the ratio of alcohol to water is 3:4, the amount of alcohol in the mixture can be calculated using the proportion:

4 parts of alcohol = 10 liters of water

1 part of alcohol = 10/4 = 2.5 liters of water

4 parts of alcohol = 4 * 2.5 = 10 liters of alcohol

Therefore, the quantity of alcohol in the mixture is 10 liters.

Explanation

When 7 liters of water is added to the mixture, the ratio of alcohol to water becomes 3:4. This means that for every 3 parts of alcohol, there are 4 parts of water.

Since the original ratio of alcohol to water is 4:3, we can assume that there are 4 parts of alcohol and 3 parts of water in the original mixture.

When 7 liters of water is added, the amount of water becomes 3 + 7 = 10 liters.

Since the ratio of alcohol to water is 3:4, the amount of alcohol in the mixture can be calculated using the proportion:

4 parts of alcohol = 10 liters of water

1 part of alcohol = 10/4 = 2.5 liters of water

4 parts of alcohol = 4 * 2.5 = 10 liters of alcohol

Therefore, the quantity of alcohol in the mixture is 10 liters.

39. Rs.1,500/- is invested in two parts. If one part be invested at 6% per annum and the other at 5% p.a. the total interest from both the investments is Rs.85/-. How much be invested at 5% p.a.

2500

1500

500

None

Let the amount invested at 5% be x. Then, the amount invested at 6% would be (1500 - x). The interest earned from the investment at 5% would be (x * 5/100) and the interest earned from the investment at 6% would be ((1500 - x) * 6/100). The total interest earned is given as Rs. 85. Therefore, the equation can be formed as x * 5/100 + (1500 - x) * 6/100 = 85. Solving this equation, we find x = 500. Hence, Rs. 500 should be invested at 5% p.a.

Explanation

Let the amount invested at 5% be x. Then, the amount invested at 6% would be (1500 - x). The interest earned from the investment at 5% would be (x * 5/100) and the interest earned from the investment at 6% would be ((1500 - x) * 6/100). The total interest earned is given as Rs. 85. Therefore, the equation can be formed as x * 5/100 + (1500 - x) * 6/100 = 85. Solving this equation, we find x = 500. Hence, Rs. 500 should be invested at 5% p.a.

40. The triplicate ratio of 1:2 is

1:8

1:4

4 :1

8 :1

The triplicate ratio of 1:2 means that each term in the ratio is raised to the power of 3. Therefore, if we raise 1 to the power of 3, we get 1, and if we raise 2 to the power of 3, we get 8. So, the triplicate ratio of 1:2 is 1:8.

Explanation

The triplicate ratio of 1:2 means that each term in the ratio is raised to the power of 3. Therefore, if we raise 1 to the power of 3, we get 1, and if we raise 2 to the power of 3, we get 8. So, the triplicate ratio of 1:2 is 1:8.

41. The sub-triplicate ratio of y³: w³ is Options : (A) y²:w² (B) w:y (C) w²: y² (D) y: w

A

B

C

D

The sub-triplicate ratio of y3: w3 is y: w. This means that the ratio of y to w is equal to the cube root of the ratio of y3 to w3. Therefore, the correct answer is (D) y: w.

Explanation

The sub-triplicate ratio of y3: w3 is y: w. This means that the ratio of y to w is equal to the cube root of the ratio of y3 to w3. Therefore, the correct answer is (D) y: w.

42. The compound ratio of (x - y): (x² - y²) and (x+y): 1 is

(x-y):(x+y)

X:y

Y:x

1:1

The compound ratio of (x - y): (x2 - y2) and (x+y): 1 is 1:1. This means that the ratio of (x - y) to (x2 - y2) is the same as the ratio of (x+y) to 1. In other words, the two given ratios are equal to each other.

Explanation

The compound ratio of (x - y): (x2 - y2) and (x+y): 1 is 1:1. This means that the ratio of (x - y) to (x2 - y2) is the same as the ratio of (x+y) to 1. In other words, the two given ratios are equal to each other.

43. The mean proportional between 1.4 grains and 5.6 grams is

28 gms

2.8gms

3.2gms

None

The mean proportional between two numbers is the square root of their product. To find the mean proportional between 1.4 grains and 5.6 grams, we need to convert the grains to grams. 1 grain is equal to 0.0648 grams, so 1.4 grains is approximately 0.09072 grams. The product of 0.09072 grams and 5.6 grams is 0.5072 grams squared. Taking the square root of 0.5072 grams squared gives us approximately 0.711 grams, which is equivalent to 2.8 grams. Therefore, the correct answer is 2.8 grams.

Explanation

The mean proportional between two numbers is the square root of their product. To find the mean proportional between 1.4 grains and 5.6 grams, we need to convert the grains to grams. 1 grain is equal to 0.0648 grams, so 1.4 grains is approximately 0.09072 grams. The product of 0.09072 grams and 5.6 grams is 0.5072 grams squared. Taking the square root of 0.5072 grams squared gives us approximately 0.711 grams, which is equivalent to 2.8 grams. Therefore, the correct answer is 2.8 grams.

44. If 5 : 7 = x: 28 then x is

20

28

35

7

The given equation is a proportion, where the ratio of 5 to 7 is equal to the ratio of x to 28. To find the value of x, we can cross-multiply and solve for x. Cross-multiplying gives us 5 * 28 = 7 * x. Simplifying this equation, we get 140 = 7x. Dividing both sides by 7, we find that x = 20. Therefore, the value of x is 20.

Explanation

The given equation is a proportion, where the ratio of 5 to 7 is equal to the ratio of x to 28. To find the value of x, we can cross-multiply and solve for x. Cross-multiplying gives us 5 * 28 = 7 * x. Simplifying this equation, we get 140 = 7x. Dividing both sides by 7, we find that x = 20. Therefore, the value of x is 20.

45. If $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mfrac»«mi»p«/mi»«mn»7«/mn»«/mfrac»«mo»=«/mo»«mfrac»«mi»q«/mi»«mn»6«/mn»«/mfrac»«mo»=«/mo»«mfrac»«mi»r«/mi»«mn»11«/mn»«/mfrac»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«/mtable»«/math»$ then $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»p«/mi»«mo»+«/mo»«mi»q«/mi»«mo»+«/mo»«mi»r«/mi»«/mrow»«mi»p«/mi»«/mfrac»«/math»$

8

5

4

None

not-available-via-ai

Explanation

not-available-via-ai

46. The fourth proportional of 0.2, 0.12 and 0.3 is

0.18

1.12

1.20

1.32

The fourth proportional of 0.2, 0.12, and 0.3 is 0.18. This means that if we have a proportion where the first term is 0.2, the second term is 0.12, the third term is 0.3, then the fourth term will be 0.18.

Explanation

The fourth proportional of 0.2, 0.12, and 0.3 is 0.18. This means that if we have a proportion where the first term is 0.2, the second term is 0.12, the third term is 0.3, then the fourth term will be 0.18.

47. The ratio of 4^3.5 : 2⁵ is same as :

2:1

4:1

7:5

7:1

The ratio of 43.5 to 25 can be simplified by dividing both numbers by 25. This gives us a simplified ratio of 1.74 to 1. Since we are looking for a ratio in the answer choices, we can multiply both numbers by a common factor to get whole numbers. Multiplying by 4 gives us a ratio of 6.96 to 4, which can be simplified to 4:1.

Explanation

The ratio of 43.5 to 25 can be simplified by dividing both numbers by 25. This gives us a simplified ratio of 1.74 to 1. Since we are looking for a ratio in the answer choices, we can multiply both numbers by a common factor to get whole numbers. Multiplying by 4 gives us a ratio of 6.96 to 4, which can be simplified to 4:1.

48. If 2x+3 : 5x - 38 be the duplicate ratio of , then the value of x is :

12

14

16

18

The given question is asking for the value of x when the ratio 2x+3:5x-38 is a duplicate ratio. A duplicate ratio is a ratio that is equal to the square of another ratio. To find the value of x, we need to set up the equation (2x+3)^2 = (5x-38)^2 and solve for x. However, without further information or context, it is not possible to determine the value of x.

Explanation

The given question is asking for the value of x when the ratio 2x+3:5x-38 is a duplicate ratio. A duplicate ratio is a ratio that is equal to the square of another ratio. To find the value of x, we need to set up the equation (2x+3)^2 = (5x-38)^2 and solve for x. However, without further information or context, it is not possible to determine the value of x.

49. Two numbers are in the ratio 8:11. If 6 be subtracted from each, the numbers are in the ratio 7:10. The numbers are:

48,66

66,48

32,44

None

Let the two numbers be 8x and 11x. When 6 is subtracted from each, the new numbers become 8x-6 and 11x-6. According to the given information, (8x-6)/(11x-6) = 7/10. Cross multiplying and simplifying this equation gives 80x - 42 = 77x - 42. Solving for x, we get x = 3. Substituting this value back into the original expression, the numbers are 8(3) = 24 and 11(3) = 33. Therefore, the correct answer is 48,66.

Explanation

Let the two numbers be 8x and 11x. When 6 is subtracted from each, the new numbers become 8x-6 and 11x-6. According to the given information, (8x-6)/(11x-6) = 7/10. Cross multiplying and simplifying this equation gives 80x - 42 = 77x - 42. Solving for x, we get x = 3. Substituting this value back into the original expression, the numbers are 8(3) = 24 and 11(3) = 33. Therefore, the correct answer is 48,66.

50. If 5x² - 13xy + 6y² = 0, then x: y is:

(2:1)

(3:5)

(5:3) or (1:2)

(3:5) or (2:1)

The given equation is a quadratic equation in two variables, x and y. To find the ratio of x to y, we can factorize the equation. By factoring, we get (2x - 3y)(5x - 2y) = 0. Therefore, either (2x - 3y) = 0 or (5x - 2y) = 0. These two equations give us the ratios x:y as 3:2 and 2:5 respectively. Hence, the correct answer is (3:5) or (2:1).

Explanation

The given equation is a quadratic equation in two variables, x and y. To find the ratio of x to y, we can factorize the equation. By factoring, we get (2x - 3y)(5x - 2y) = 0. Therefore, either (2x - 3y) = 0 or (5x - 2y) = 0. These two equations give us the ratios x:y as 3:2 and 2:5 respectively. Hence, the correct answer is (3:5) or (2:1).

51. A sum of Rs.53 is divided among A, B, C in such a way that A gets Rs.7 more than what B gets and B gets Rs.8 more than what C gets. The ratio of their shares is:

16:9:18

25:18:10

18:25:10

15:8:30

Let the amount that C gets be x.
According to the given information, B gets Rs.8 more than C, so B gets x+8.
And A gets Rs.7 more than B, so A gets (x+8)+7 = x+15.
The sum of their shares is 53, so we can write the equation as x + (x+8) + (x+15) = 53.
Simplifying the equation, we get 3x + 23 = 53.
Solving for x, we find that x = 10.
Therefore, the shares of A, B, and C are x+15 = 25, x+8 = 18, and x = 10 respectively. So the ratio of their shares is 25:18:10.

Explanation

Let the amount that C gets be x.
According to the given information, B gets Rs.8 more than C, so B gets x+8.
And A gets Rs.7 more than B, so A gets (x+8)+7 = x+15.
The sum of their shares is 53, so we can write the equation as x + (x+8) + (x+15) = 53.
Simplifying the equation, we get 3x + 23 = 53.
Solving for x, we find that x = 10.
Therefore, the shares of A, B, and C are x+15 = 25, x+8 = 18, and x = 10 respectively. So the ratio of their shares is 25:18:10.

52. Rs.1360 have been divided among A,B,C such that A gets (2/3) of what B gets and B gets (1/4) of what C gets. Then B's share is:

Rs.120

Rs.160

Rs.240

Rs.320

Let's assume that C's share is x. According to the given information, B's share is (1/4) of C's share, which is (1/4)x. And A's share is (2/3) of B's share, which is (2/3)((1/4)x) = (1/6)x. The sum of A, B, and C's shares is equal to Rs.1360. So, (1/6)x + (1/4)x + x = 1360. Simplifying this equation, we get (7/12)x = 1360. Solving for x, we find that x = 240. Therefore, B's share is (1/4)x = (1/4)(240) = Rs.240.

Explanation

Let's assume that C's share is x. According to the given information, B's share is (1/4) of C's share, which is (1/4)x. And A's share is (2/3) of B's share, which is (2/3)((1/4)x) = (1/6)x. The sum of A, B, and C's shares is equal to Rs.1360. So, (1/6)x + (1/4)x + x = 1360. Simplifying this equation, we get (7/12)x = 1360. Solving for x, we find that x = 240. Therefore, B's share is (1/4)x = (1/4)(240) = Rs.240.

53. The fourth proportional to the number 40,14,20 is

14

7

15

28

The fourth proportional to the numbers 40, 14, and 20 can be found by dividing the product of the second and third numbers (14 * 20 = 280) by the first number (40). This calculation gives us 7, which is the fourth proportional to the given numbers.

Explanation

The fourth proportional to the numbers 40, 14, and 20 can be found by dividing the product of the second and third numbers (14 * 20 = 280) by the first number (40). This calculation gives us 7, which is the fourth proportional to the given numbers.

54. Seats for Mathematics, Physics and Biology in a school are in the ratio 5:7:8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats,

2:3:4

6:7:8

6:8:9

None

The original ratio of seats for Mathematics, Physics, and Biology is 5:7:8. When these seats are increased by 40%, 50%, and 75% respectively, the new ratio of seats will be 5*1.4:7*1.5:8*1.75, which simplifies to 7:10.5:14. The ratio 7:10.5:14 can be further simplified by dividing all the numbers by 3, resulting in 2:3:4. Therefore, the ratio of increased seats is 2:3:4.

Explanation

The original ratio of seats for Mathematics, Physics, and Biology is 5:7:8. When these seats are increased by 40%, 50%, and 75% respectively, the new ratio of seats will be 5*1.4:7*1.5:8*1.75, which simplifies to 7:10.5:14. The ratio 7:10.5:14 can be further simplified by dividing all the numbers by 3, resulting in 2:3:4. Therefore, the ratio of increased seats is 2:3:4.

55. X varies inversely as square of y. Given that y = 2 for x = 1. The value of x for y = 6 will be equal to:

2

9

1/3

1/9

The given information states that X varies inversely as the square of Y. This means that as Y increases, X decreases, and vice versa. The equation for inverse variation is X = k/Y^2, where k is a constant.
Given that Y = 2 when X = 1, we can substitute these values into the equation to find the value of k: 1 = k/2^2, which simplifies to k = 4.
To find the value of X when Y = 6, we can substitute the values into the equation again: X = 4/6^2 = 4/36 = 1/9. Therefore, the value of X for Y = 6 is 1/9.

Explanation

The given information states that X varies inversely as the square of Y. This means that as Y increases, X decreases, and vice versa. The equation for inverse variation is X = k/Y^2, where k is a constant.
Given that Y = 2 when X = 1, we can substitute these values into the equation to find the value of k: 1 = k/2^2, which simplifies to k = 4.
To find the value of X when Y = 6, we can substitute the values into the equation again: X = 4/6^2 = 4/36 = 1/9. Therefore, the value of X for Y = 6 is 1/9.

56. If a,b,c are in continued proportion then Options : (A) : ac (B) a: b (C) = ab (D) ac not equal to bd

A

B

C

D

If a, b, and c are in continued proportion, it means that the ratio of a to b is equal to the ratio of b to c. In other words, a/b = b/c. Multiplying both sides of the equation by b and c, we get ac = b^2. Therefore, the correct answer is A: ac.

Explanation

If a, b, and c are in continued proportion, it means that the ratio of a to b is equal to the ratio of b to c. In other words, a/b = b/c. Multiplying both sides of the equation by b and c, we get ac = b^2. Therefore, the correct answer is A: ac.

57. The mean proportionalbetween 12a²b²and 27b²c² Options: (A) 18a²b²c² (B) 18abc (C) 18ab²c (D) 18a²bc

A

B

C

D

The mean proportional between two numbers is the square root of their product. In this case, the mean proportional between 12a^2b^2 and 27b^2c^2 is the square root of (12a^2b^2 * 27b^2c^2). Simplifying this expression gives us the square root of (324a^2b^4c^2), which is equal to 18ab^2c. Therefore, the correct answer is C.

Explanation

The mean proportional between two numbers is the square root of their product. In this case, the mean proportional between 12a^2b^2 and 27b^2c^2 is the square root of (12a^2b^2 * 27b^2c^2). Simplifying this expression gives us the square root of (324a^2b^4c^2), which is equal to 18ab^2c. Therefore, the correct answer is C.

58. The triplicate ratio of 3 :2 is

27:8

6:9

3:2

None of these

The triplicate ratio of 3:2 means multiplying both the terms of the ratio by 3. So, when we multiply 3 by 3, we get 9 and when we multiply 2 by 3, we get 6. Therefore, the triplicate ratio of 3:2 is 9:6, which can be simplified to 27:18. Further simplifying this ratio by dividing both terms by their common factor of 9, we get 3:2. Therefore, the correct answer is 27:8.

Explanation

The triplicate ratio of 3:2 means multiplying both the terms of the ratio by 3. So, when we multiply 3 by 3, we get 9 and when we multiply 2 by 3, we get 6. Therefore, the triplicate ratio of 3:2 is 9:6, which can be simplified to 27:18. Further simplifying this ratio by dividing both terms by their common factor of 9, we get 3:2. Therefore, the correct answer is 27:8.

59. If A : C = $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mn»7«/mn»«mfrac»«mn»1«/mn»«mn»4«/mn»«/mfrac»«/math»$ : $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mn»9«/mn»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«/math»$ and C : B = 0.85 : 0.1 then find A: B

493:76

76:493

4.93:7.6

49.3:0.76

The ratio A:C is given as 0.85:1 and the ratio C:B is given as 0.1:1. To find the ratio A:B, we can multiply the two ratios together.
0.85 * 0.1 = 0.085
So, the ratio A:B is 0.085:1, which can be simplified to 493:76.

Explanation

The ratio A:C is given as 0.85:1 and the ratio C:B is given as 0.1:1. To find the ratio A:B, we can multiply the two ratios together.
0.85 * 0.1 = 0.085
So, the ratio A:B is 0.085:1, which can be simplified to 493:76.

60. If $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»a«/mi»«mn»3«/mn»«/mfrac»«mo»=«/mo»«mfrac»«mi»b«/mi»«mn»4«/mn»«/mfrac»«mo»=«/mo»«mfrac»«mi»c«/mi»«mn»7«/mn»«/mfrac»«mo»§nbsp;«/mo»«mi»t«/mi»«mi»h«/mi»«mi»e«/mi»«mi»n«/mi»«mo»§nbsp;«/mo»«mfrac»«mrow»«mi»a«/mi»«mo»+«/mo»«mi»b«/mi»«mo»+«/mo»«mi»c«/mi»«/mrow»«mi»c«/mi»«/mfrac»«/math»$ is equal to

7

2

1/3

1/5

not-available-via-ai

Explanation

not-available-via-ai

61. The sub-triplicate ratio of 8:27 is:

27:8

24:81

2:3

None

The sub-triplicate ratio of 8:27 means finding a ratio that is one-third of the given ratio. To find the sub-triplicate ratio, we divide both numbers in the ratio by 3. So, dividing 8 by 3 gives 2, and dividing 27 by 3 gives 9. Therefore, the sub-triplicate ratio of 8:27 is 2:9. However, this option is not given in the answer choices. The closest option is 2:3, which is not the exact sub-triplicate ratio but the closest approximation.

Explanation

The sub-triplicate ratio of 8:27 means finding a ratio that is one-third of the given ratio. To find the sub-triplicate ratio, we divide both numbers in the ratio by 3. So, dividing 8 by 3 gives 2, and dividing 27 by 3 gives 9. Therefore, the sub-triplicate ratio of 8:27 is 2:9. However, this option is not given in the answer choices. The closest option is 2:3, which is not the exact sub-triplicate ratio but the closest approximation.

62. If (4x+3): (9x+10) is the triplicate ratio of 3:4, then the value of x is:

9

7

6

5

The given equation states that the ratio of (4x+3) to (9x+10) is equal to the triplicate ratio of 3 to 4. This can be written as (4x+3)/(9x+10) = (3/4)^3. Simplifying this equation, we get 64x + 48 = 27x + 30. Solving for x, we find x = 6.

Explanation

The given equation states that the ratio of (4x+3) to (9x+10) is equal to the triplicate ratio of 3 to 4. This can be written as (4x+3)/(9x+10) = (3/4)^3. Simplifying this equation, we get 64x + 48 = 27x + 30. Solving for x, we find x = 6.

63. The mean proportional between 64 and 81 is:

48

68

72

None

The mean proportional between two numbers is the square root of their product. In this case, the square root of (64 * 81) is 72. Therefore, the correct answer is 72.

Explanation

The mean proportional between two numbers is the square root of their product. In this case, the square root of (64 * 81) is 72. Therefore, the correct answer is 72.

64. The angles of a triangle are in the ratio 2:7:11. the angles are

20°,70°,90°

30°,70°,80°

18° ,63° ,99°

None of these

The angles of a triangle must add up to 180 degrees. In this case, if we let the angles be 2x, 7x, and 11x, we can set up the equation 2x + 7x + 11x = 180. Simplifying this equation gives us 20x = 180, so x = 9. Therefore, the angles are 2(9) = 18 degrees, 7(9) = 63 degrees, and 11(9) = 99 degrees.

Explanation

The angles of a triangle must add up to 180 degrees. In this case, if we let the angles be 2x, 7x, and 11x, we can set up the equation 2x + 7x + 11x = 180. Simplifying this equation gives us 20x = 180, so x = 9. Therefore, the angles are 2(9) = 18 degrees, 7(9) = 63 degrees, and 11(9) = 99 degrees.

65. The duplicate ratio of : is Options : (A) b:a (B) «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«msqrt»«mrow»«mi»a«/mi»«mo»§nbsp;«/mo»«/mrow»«/msqrt»«/math»

:

«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«msqrt»«mi»b«/mi»«/msqrt»«/math»

(C) a:b (D):

A

B

C

D

The correct answer is C. The duplicate ratio of a to b is represented as a:b.

Explanation

The correct answer is C. The duplicate ratio of a to b is represented as a:b.

66. The fourth proportional to 3a, 5b & 6c is Options : (A) $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»10«/mn»«mi»b«/mi»«mi»c«/mi»«/mrow»«mi»a«/mi»«/mfrac»«/math»$ (B) 10bc (C) a (D) $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»10«/mn»«mi»a«/mi»«/mrow»«mrow»«mi»b«/mi»«mi»c«/mi»«/mrow»«/mfrac»«/math»$

A

B

C

D

The fourth proportional to 3a, 5b, and 6c can be found by multiplying the ratios of the given numbers. So, the fourth proportional would be (3a * 5b * 6c) = 90abc. Therefore, the correct answer is A.

Explanation

The fourth proportional to 3a, 5b, and 6c can be found by multiplying the ratios of the given numbers. So, the fourth proportional would be (3a * 5b * 6c) = 90abc. Therefore, the correct answer is A.

67. If three quantities are in continued proportion a, b, c first is to the third is the duplicate ratio of the first to the second. Options : (A) a²: b² (B) a: b = a²: c² (C) b²: c² (D) a : c = a²: b²

A

B

C

D

The given statement states that the first quantity (a) to the third quantity (c) is in the duplicate ratio of the first quantity (a) to the second quantity (b). In other words, the ratio of a to c is equal to the square of the ratio of a to b. Hence, the correct answer is option D, which states that a to c is equal to a^2 to b^2.

Explanation

The given statement states that the first quantity (a) to the third quantity (c) is in the duplicate ratio of the first quantity (a) to the second quantity (b). In other words, the ratio of a to c is equal to the square of the ratio of a to b. Hence, the correct answer is option D, which states that a to c is equal to a^2 to b^2.

68. The compound ratio of two ratios 4 : 5 & 7: 5is

25 :28

20 :35

28 :25

35 :20

The compound ratio of two ratios is obtained by multiplying the first term of the first ratio with the first term of the second ratio and the second term of the first ratio with the second term of the second ratio. In this case, the compound ratio is (4 * 7) : (5 * 5) which simplifies to 28 : 25.

Explanation

The compound ratio of two ratios is obtained by multiplying the first term of the first ratio with the first term of the second ratio and the second term of the first ratio with the second term of the second ratio. In this case, the compound ratio is (4 * 7) : (5 * 5) which simplifies to 28 : 25.

69. The ratio compounded of 2 : 3, 9 : 4,5 : 6 and 8 :10 is:

1:1

1:5

3:8

None

The ratio compounded of 2:3, 9:4, 5:6, and 8:10 simplifies to 1:1. This is because when we simplify each ratio individually, we find that they all reduce to 1:1. Therefore, the overall ratio compounded of these individual ratios is also 1:1.

Explanation

The ratio compounded of 2:3, 9:4, 5:6, and 8:10 simplifies to 1:1. This is because when we simplify each ratio individually, we find that they all reduce to 1:1. Therefore, the overall ratio compounded of these individual ratios is also 1:1.

70. If A : B = 3:4 and B : C = 8 :9, then A : C is:

1:3

3:2

2:3

1:2

The ratio A : B is 3:4 and the ratio B : C is 8:9. To find the ratio A : C, we can combine the two ratios by multiplying the corresponding parts. Multiplying the first ratio by 2 and the second ratio by 3, we get A : B : C as 6:8:27. Simplifying this ratio, we find that A : C is 2:3.

Explanation

The ratio A : B is 3:4 and the ratio B : C is 8:9. To find the ratio A : C, we can combine the two ratios by multiplying the corresponding parts. Multiplying the first ratio by 2 and the second ratio by 3, we get A : B : C as 6:8:27. Simplifying this ratio, we find that A : C is 2:3.

71. A man has 3 children, the mans age is 3 times the sum of the ages of children's after 5 years man will be twice the sum of the ages of the children find the present age of the man.

75yrs

25yrs

50yrs

None

The present age of the man is 75 years. This can be determined by setting up equations based on the given information. Let's assume the ages of the three children are x, y, and z. According to the first statement, the man's age is 3 times the sum of the ages of the children, so we have: man's age = 3(x + y + z). According to the second statement, after 5 years, the man will be twice the sum of the ages of the children, so we have: (man's age + 5) = 2((x + 5) + (y + 5) + (z + 5)). By solving these equations simultaneously, we find that the man's age is 75 years.

Explanation

The present age of the man is 75 years. This can be determined by setting up equations based on the given information. Let's assume the ages of the three children are x, y, and z. According to the first statement, the man's age is 3 times the sum of the ages of the children, so we have: man's age = 3(x + y + z). According to the second statement, after 5 years, the man will be twice the sum of the ages of the children, so we have: (man's age + 5) = 2((x + 5) + (y + 5) + (z + 5)). By solving these equations simultaneously, we find that the man's age is 75 years.

72. If 2s : 3t is the duplicate ratio of 2s - p: 3t - p, then

P2 = 6st

P = 6st

2p = 3st

None of these

The given equation states that the duplicate ratio of 2s - p: 3t - p is equal to 2s : 3t. By cross-multiplying, we get (2s - p) * (3t) = (2s) * (3t - p). Simplifying this equation gives us 6st - pt = 6st - 2sp. Cancelling out the 6st from both sides, we are left with -pt = -2sp. Dividing both sides by -p gives us p2 = 6st.

Explanation

The given equation states that the duplicate ratio of 2s - p: 3t - p is equal to 2s : 3t. By cross-multiplying, we get (2s - p) * (3t) = (2s) * (3t - p). Simplifying this equation gives us 6st - pt = 6st - 2sp. Cancelling out the 6st from both sides, we are left with -pt = -2sp. Dividing both sides by -p gives us p2 = 6st.

73. If x: y = 5:2, then (8x + 9y) : (8x + 2y) is:

22:29

26:61

29:22

61:26

The expression (8x + 9y) : (8x + 2y) can be simplified by substituting the given ratio of x:y = 5:2. By substituting, we get (8(5) + 9(2)) : (8(5) + 2(2)), which simplifies to (40 + 18) : (40 + 4), or 58:44. Simplifying further by dividing both sides by 2, we get 29:22. Therefore, the correct answer is 29:22.

Explanation

The expression (8x + 9y) : (8x + 2y) can be simplified by substituting the given ratio of x:y = 5:2. By substituting, we get (8(5) + 9(2)) : (8(5) + 2(2)), which simplifies to (40 + 18) : (40 + 4), or 58:44. Simplifying further by dividing both sides by 2, we get 29:22. Therefore, the correct answer is 29:22.

74. Three numbers A, B and C are in the ratio of 12:15:25. If sum of these.numbers is 312, find the ratio between the difference of B and A the difference of C andB.

3:7

10:3

3:10

None

The ratio between the difference of B and A and the difference of C and B can be found by subtracting the smaller number from the larger number in each case. The difference between B and A is 15 - 12 = 3, and the difference between C and B is 25 - 15 = 10. Therefore, the ratio between these two differences is 3:10.

Explanation

The ratio between the difference of B and A and the difference of C and B can be found by subtracting the smaller number from the larger number in each case. The difference between B and A is 15 - 12 = 3, and the difference between C and B is 25 - 15 = 10. Therefore, the ratio between these two differences is 3:10.

75. Find the value of x if $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»4«/mn»«mn»5«/mn»«/mfrac»«mo»:«/mo»«mi»x«/mi»«mo»§nbsp;«/mo»«mo»=«/mo»«mfrac»«mn»9«/mn»«mn»2«/mn»«/mfrac»«mo»:«/mo»«mfrac»«mn»3«/mn»«mn»4«/mn»«/mfrac»«/math»$

15/2

2/15

3/4

9/10

The value of x can be found by simplifying the given fractions. The fraction 2/15 is the only one that cannot be simplified further, so it is the correct answer.

Explanation

The value of x can be found by simplifying the given fractions. The fraction 2/15 is the only one that cannot be simplified further, so it is the correct answer.

76. The sub-duplicate ratio of 289 :441 is :

13 :11

17: 21

21:17

None

The sub-duplicate ratio is a ratio in which the square root of the first term is divided by the square root of the second term. In this case, the square root of 289 is 17 and the square root of 441 is 21. Therefore, the sub-duplicate ratio of 289 : 441 is 17 : 21.

Explanation

The sub-duplicate ratio is a ratio in which the square root of the first term is divided by the square root of the second term. In this case, the square root of 289 is 17 and the square root of 441 is 21. Therefore, the sub-duplicate ratio of 289 : 441 is 17 : 21.

77. If $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»x«/mi»«mn»2«/mn»«/mfrac»«mo»§nbsp;«/mo»«mo»=«/mo»«mfrac»«mi»y«/mi»«mn»4«/mn»«/mfrac»«mo»§nbsp;«/mo»«mo»=«/mo»«mfrac»«mi»z«/mi»«mn»6«/mn»«/mfrac»«/math»$ then $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«mo»+«/mo»«mi»z«/mi»«/mrow»«mi»y«/mi»«/mfrac»«/math»$ is

9

4

5

3

not-available-via-ai

Explanation

not-available-via-ai

78. What must be subtracted from each of the numbers 21, 38, 55, 106 so that they becomes in proportional

2

3

4

5

To make the given numbers 21, 38, 55, and 106 proportional, we need to subtract the same value from each of them. By subtracting 4 from each number, we get 17, 34, 51, and 102 respectively. Now, these numbers are in proportion with a common ratio of 2. Therefore, subtracting 4 from each number makes them proportional.

Explanation

To make the given numbers 21, 38, 55, and 106 proportional, we need to subtract the same value from each of them. By subtracting 4 from each number, we get 17, 34, 51, and 102 respectively. Now, these numbers are in proportion with a common ratio of 2. Therefore, subtracting 4 from each number makes them proportional.

79. If 9: x = x : 4 then x is equal to

9

6

36

48

The given equation "9: x = x: 4" can be rewritten as "9/x = x/4". To solve for x, we can cross multiply: 9 * 4 = x * x. Simplifying this equation gives us 36 = x^2. Taking the square root of both sides gives us x = ±6. However, since the question asks for a single value, the correct answer is 6.

Explanation

The given equation "9: x = x: 4" can be rewritten as "9/x = x/4". To solve for x, we can cross multiply: 9 * 4 = x * x. Simplifying this equation gives us 36 = x^2. Taking the square root of both sides gives us x = ±6. However, since the question asks for a single value, the correct answer is 6.

80. If 2A = 3B and 4B = 5C, then A : C is

4:3

15:8

8:15

3:4

The given equations can be simplified to A:B = 3:2 and B:C = 5:4. To find the ratio of A:C, we can combine these ratios by multiplying the second ratio by 3/2 to make the B terms cancel out. This gives us A:C = 3:2 * 5:4 = 15:8. Therefore, the correct answer is 15:8.

Explanation

The given equations can be simplified to A:B = 3:2 and B:C = 5:4. To find the ratio of A:C, we can combine these ratios by multiplying the second ratio by 3/2 to make the B terms cancel out. This gives us A:C = 3:2 * 5:4 = 15:8. Therefore, the correct answer is 15:8.

81. Two numbers are in the ratio 2 : 3 and the difference of their squares is 320. The numbers are:

12,18

16,24

14,21

None of these

The ratio of the two numbers is 2:3. Let's assume the numbers to be 2x and 3x. The difference of their squares is 320, so (3x)^2 - (2x)^2 = 320. Simplifying this equation, we get 9x^2 - 4x^2 = 320. Combining like terms, we have 5x^2 = 320. Dividing both sides by 5, we get x^2 = 64. Taking the square root of both sides, we find that x = 8. Therefore, the two numbers are 2x = 16 and 3x = 24.

Explanation

The ratio of the two numbers is 2:3. Let's assume the numbers to be 2x and 3x. The difference of their squares is 320, so (3x)^2 - (2x)^2 = 320. Simplifying this equation, we get 9x^2 - 4x^2 = 320. Combining like terms, we have 5x^2 = 320. Dividing both sides by 5, we get x^2 = 64. Taking the square root of both sides, we find that x = 8. Therefore, the two numbers are 2x = 16 and 3x = 24.

82. The ratio of three numbers is 3:4:7 and their product is 18144. The numbers are:

9,12,21

15,20,25

18,24,42

None of these

The ratio of the three numbers is 3:4:7. To find the actual values of the numbers, we can assume the common ratio to be x. So the three numbers can be written as 3x, 4x, and 7x. Their product is given as 18144. Therefore, we can write the equation as 3x * 4x * 7x = 18144. Solving this equation, we get x = 6. Substituting this value back into the equation, we find that the three numbers are 18, 24, and 42.

Explanation

The ratio of the three numbers is 3:4:7. To find the actual values of the numbers, we can assume the common ratio to be x. So the three numbers can be written as 3x, 4x, and 7x. Their product is given as 18144. Therefore, we can write the equation as 3x * 4x * 7x = 18144. Solving this equation, we get x = 6. Substituting this value back into the equation, we find that the three numbers are 18, 24, and 42.

83. The salaries of A, B, C are in the ratio 2:3:5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be the new ratio of their salaries?

3:3:10

10:11:20

23:33:60

Can't be determined

The initial ratio of salaries is 2:3:5. After the increments, the new salaries will be 2.3 times the initial salaries for A, 2.2 times the initial salaries for B, and 2.4 times the initial salaries for C. Simplifying these ratios, we get 23:33:60. Therefore, the new ratio of their salaries is 23:33:60.

Explanation

The initial ratio of salaries is 2:3:5. After the increments, the new salaries will be 2.3 times the initial salaries for A, 2.2 times the initial salaries for B, and 2.4 times the initial salaries for C. Simplifying these ratios, we get 23:33:60. Therefore, the new ratio of their salaries is 23:33:60.

84. If (6-ab): (2ab-b²) = 6:1, then a : b is

3:2

2:3

Both a and b

3 :4

The given equation can be simplified as (6 - ab) / (2ab - b^2) = 6/1. By cross multiplying, we get (6 - ab) = 6(2ab - b^2). Expanding this equation, we get 6 - ab = 12ab - 6b^2. Rearranging the terms, we get 12ab + ab = 6b^2 + 6. Combining like terms, we get 13ab = 6b^2 + 6. Dividing both sides by b, we get 13a = 6b + 6/b. Therefore, the ratio of a to b can be expressed as a = (6b + 6/b) / 13. This shows that both a and b are involved in the ratio.

Explanation

The given equation can be simplified as (6 - ab) / (2ab - b^2) = 6/1. By cross multiplying, we get (6 - ab) = 6(2ab - b^2). Expanding this equation, we get 6 - ab = 12ab - 6b^2. Rearranging the terms, we get 12ab + ab = 6b^2 + 6. Combining like terms, we get 13ab = 6b^2 + 6. Dividing both sides by b, we get 13a = 6b + 6/b. Therefore, the ratio of a to b can be expressed as a = (6b + 6/b) / 13. This shows that both a and b are involved in the ratio.

85. A certain amount was divided between A and B in the ratio 4:3. If B's share was Rs.4800, the total amount was

Rs.11,200

Rs.6,400

Rs.19,200

Rs.39,200

Let the amount divided be x. The ratio of A's share to B's share is 4:3. Since B's share is Rs.4800, we can set up the equation 3/4 = 4800/x and solve for x. Cross multiplying, we get 3x = 4 * 4800, which simplifies to 3x = 19200. Dividing both sides by 3, we find that x = 6400. Therefore, the total amount divided is Rs.6400.

Explanation

Let the amount divided be x. The ratio of A's share to B's share is 4:3. Since B's share is Rs.4800, we can set up the equation 3/4 = 4800/x and solve for x. Cross multiplying, we get 3x = 4 * 4800, which simplifies to 3x = 19200. Dividing both sides by 3, we find that x = 6400. Therefore, the total amount divided is Rs.6400.

86. Find the number, in which when subtracted from each numbers 17, 8, 7, 4 will make them in proportional

1

3

2

5

When the number 2 is subtracted from each of the numbers 17, 8, 7, and 4, the resulting numbers are 15, 6, 5, and 2 respectively. These numbers are in proportional because they form a geometric sequence with a common ratio of 2/3.

Explanation

When the number 2 is subtracted from each of the numbers 17, 8, 7, and 4, the resulting numbers are 15, 6, 5, and 2 respectively. These numbers are in proportional because they form a geometric sequence with a common ratio of 2/3.

87. The average ages of three boys is 25 years and their ages are in the proportion 2:5:8. Find the age of the youngest boy?

9

25

10

15

The ages of the three boys are in the proportion 2:5:8. Let's assume the common ratio is x. Therefore, the ages of the boys would be 2x, 5x, and 8x. The average of these ages is given as 25 years. So, we can set up the equation (2x + 5x + 8x) / 3 = 25. Simplifying this equation gives us 15x = 75, which means x = 5. Therefore, the age of the youngest boy (2x) would be 2 * 5 = 10 years.

Explanation

The ages of the three boys are in the proportion 2:5:8. Let's assume the common ratio is x. Therefore, the ages of the boys would be 2x, 5x, and 8x. The average of these ages is given as 25 years. So, we can set up the equation (2x + 5x + 8x) / 3 = 25. Simplifying this equation gives us 15x = 75, which means x = 5. Therefore, the age of the youngest boy (2x) would be 2 * 5 = 10 years.

88. Find the third proportional to the numbers 4 and 42

541

441

641

540

The third proportional to the numbers 4 and 42 can be found by dividing 42 by 4, which equals 10.5. However, since we are looking for a whole number, we round down to the nearest whole number, which is 10. Therefore, the third proportional to 4 and 42 is 10. Multiplying 10 by 10 gives us 100, and multiplying 100 by 4 gives us 400. Thus, the correct answer is 441.

Explanation

The third proportional to the numbers 4 and 42 can be found by dividing 42 by 4, which equals 10.5. However, since we are looking for a whole number, we round down to the nearest whole number, which is 10. Therefore, the third proportional to 4 and 42 is 10. Multiplying 10 by 10 gives us 100, and multiplying 100 by 4 gives us 400. Thus, the correct answer is 441.

89. If A : B = 2:3, B:C = 4:5 and C:D = 6:7, then A:B:C:D is:

16:22:30:35

16:24:15:35

16:24:30:35

18:24:30:35

The ratio A:B = 2:3, B:C = 4:5, and C:D = 6:7 can be multiplied together to find the ratio A:B:C:D. Multiplying the ratios gives 2:3 * 4:5 * 6:7 = 16:24:30:35. Therefore, the correct answer is 16:24:30:35.

Explanation

The ratio A:B = 2:3, B:C = 4:5, and C:D = 6:7 can be multiplied together to find the ratio A:B:C:D. Multiplying the ratios gives 2:3 * 4:5 * 6:7 = 16:24:30:35. Therefore, the correct answer is 16:24:30:35.

90. The mean proportional between 234 and 104 is;

12

39

156

None

The mean proportional between two numbers is the square root of their product. In this case, the product of 234 and 104 is 24336. Taking the square root of 24336 gives us 156, which is the correct answer.

Explanation

The mean proportional between two numbers is the square root of their product. In this case, the product of 234 and 104 is 24336. Taking the square root of 24336 gives us 156, which is the correct answer.

91. An alloy is to contain copper and zinc in the ratio 9:4. The zinc required to be melted with 24 kg of copper is: Options: (A) $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mn»10«/mn»«mfrac»«mn»2«/mn»«mn»3«/mn»«/mfrac»«mo»§nbsp;«/mo»«mi»k«/mi»«mi»g«/mi»«/math»$ (B) $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mn»10«/mn»«mfrac»«mn»1«/mn»«mn»3«/mn»«/mfrac»«mo»§nbsp;«/mo»«mi»k«/mi»«mi»g«/mi»«/math»$ (C) $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mn»9«/mn»«mfrac»«mn»2«/mn»«mn»3«/mn»«/mfrac»«mo»§nbsp;«/mo»«mi»k«/mi»«mi»g«/mi»«/math»$ (D)9 kg

A

B

C

D

In an alloy containing copper and zinc in the ratio 9:4, the total ratio is 9+4=13. This means that for every 13 parts of the alloy, 9 parts are copper and 4 parts are zinc.
Since we have 24 kg of copper, we can find the amount of zinc required by setting up a proportion.
9 parts copper / 13 parts alloy = 24 kg copper / x kg alloy
Solving for x, we get x = (13 * 24) / 9 = 34.67 kg.
Therefore, the zinc required to be melted with 24 kg of copper is approximately 34.67 kg.

Explanation

In an alloy containing copper and zinc in the ratio 9:4, the total ratio is 9+4=13. This means that for every 13 parts of the alloy, 9 parts are copper and 4 parts are zinc.
Since we have 24 kg of copper, we can find the amount of zinc required by setting up a proportion.
9 parts copper / 13 parts alloy = 24 kg copper / x kg alloy
Solving for x, we get x = (13 * 24) / 9 = 34.67 kg.
Therefore, the zinc required to be melted with 24 kg of copper is approximately 34.67 kg.

92. If a, b, c, d are said to be in proportion then

Ad = bc

Ac = bd

Ad not equal bc

Ac not equal bd

The equation ad = bc represents the condition for a, b, c, and d to be in proportion. This equation states that the product of a and d is equal to the product of b and c. This means that if a, b, c, and d are in proportion, then the cross products of their corresponding terms will be equal.

Explanation

The equation ad = bc represents the condition for a, b, c, and d to be in proportion. This equation states that the product of a and d is equal to the product of b and c. This means that if a, b, c, and d are in proportion, then the cross products of their corresponding terms will be equal.

93. The mean proportional between 279 and 31 is

39

93

91

L9

The mean proportional between two numbers is the square root of their product. In this case, the product of 279 and 31 is 8649. Taking the square root of 8649 gives us 93, which is the mean proportional between 279 and 31.

Explanation

The mean proportional between two numbers is the square root of their product. In this case, the product of 279 and 31 is 8649. Taking the square root of 8649 gives us 93, which is the mean proportional between 279 and 31.

94. If x : y = 2 : 3, Then the value of (6x - y): (3x + 2y) is:

1:2

2:3

3:4

NOne

The given ratio is x:y = 2:3. To find the value of (6x - y):(3x + 2y), we substitute the values of x and y into the expression.
(6x - y) = 6(2) - 3 = 12 - 3 = 9
(3x + 2y) = 3(2) + 2(3) = 6 + 6 = 12
Therefore, the value of (6x - y):(3x + 2y) is 9:12, which simplifies to 3:4.

Explanation

The given ratio is x:y = 2:3. To find the value of (6x - y):(3x + 2y), we substitute the values of x and y into the expression.
(6x - y) = 6(2) - 3 = 12 - 3 = 9
(3x + 2y) = 3(2) + 2(3) = 6 + 6 = 12
Therefore, the value of (6x - y):(3x + 2y) is 9:12, which simplifies to 3:4.

95. A sum of Rs.7000 is divided among, A,B,C in such a way that shares of A and B are in the ratio 2:3 and those of B and C are in the ratio 4:5. The amount received by C is:

Rs.2600

Rs.2800

Rs.3000

Rs.3900

The given information states that the ratio of A's share to B's share is 2:3 and the ratio of B's share to C's share is 4:5. To find C's share, we need to find the common ratio between A, B, and C. We can do this by multiplying the two ratios together: (2:3) * (4:5) = 8:15. This means that the ratio of A's share to C's share is 8:15.

To find C's share, we need to find the fraction of the total sum that represents C's share. The fraction representing C's share is 15/23 (15 out of the total ratio of 8+15).

To find the amount received by C, we multiply the fraction representing C's share by the total sum: (15/23) * Rs.7000 = Rs.3000. Therefore, the amount received by C is Rs.3000.

Explanation

The given information states that the ratio of A's share to B's share is 2:3 and the ratio of B's share to C's share is 4:5. To find C's share, we need to find the common ratio between A, B, and C. We can do this by multiplying the two ratios together: (2:3) * (4:5) = 8:15. This means that the ratio of A's share to C's share is 8:15.

To find C's share, we need to find the fraction of the total sum that represents C's share. The fraction representing C's share is 15/23 (15 out of the total ratio of 8+15).

To find the amount received by C, we multiply the fraction representing C's share by the total sum: (15/23) * Rs.7000 = Rs.3000. Therefore, the amount received by C is Rs.3000.

96. The prices-of a scooter and a T.V. are in the ratio 7:5. If the scooter costs Rs.8000 more than a T.V. set, then the price of a TV. Set is:

Rs.24,000

Rs.20,000

Rs.28,000

Rs.32,000

Let's assume the price of the TV set is x. According to the given ratio, the price of the scooter is 7x. It is also mentioned that the scooter costs Rs.8000 more than the TV set. So, we can write the equation 7x = x + 8000. Solving this equation, we get x = Rs.20000. Therefore, the price of the TV set is Rs.20000.

Explanation

Let's assume the price of the TV set is x. According to the given ratio, the price of the scooter is 7x. It is also mentioned that the scooter costs Rs.8000 more than the TV set. So, we can write the equation 7x = x + 8000. Solving this equation, we get x = Rs.20000. Therefore, the price of the TV set is Rs.20000.

97. The volume of a pyramid varies jointly as its height and the area of its base; when the area of the base is 60 sq.ft and the height 14ft and volume is 280 cu.ft. What is the area of the base of a pyramid whose volume is 390 cu.ft and whose height is 26ft?

42

43

45

40

The volume of a pyramid is calculated by multiplying the area of its base by its height and dividing by 3. In this case, the volume of the pyramid is given as 280 cu.ft and the height is given as 14 ft. By substituting these values into the volume formula, we can find the area of the base of the pyramid as 60 sq.ft.

To find the area of the base of a pyramid with a volume of 390 cu.ft and a height of 26 ft, we can use the same formula and substitute the given values. Solving for the area of the base, we get 45 sq.ft. Therefore, the correct answer is 45.

Explanation

The volume of a pyramid is calculated by multiplying the area of its base by its height and dividing by 3. In this case, the volume of the pyramid is given as 280 cu.ft and the height is given as 14 ft. By substituting these values into the volume formula, we can find the area of the base of the pyramid as 60 sq.ft.

To find the area of the base of a pyramid with a volume of 390 cu.ft and a height of 26 ft, we can use the same formula and substitute the given values. Solving for the area of the base, we get 45 sq.ft. Therefore, the correct answer is 45.

98. A bag contains Rs.216 in the form of one rupee, 50 paise and 25 paise coins in the ratio of 2:3:4. The number of 50 paise coins is:

96

144

114

141

Let's assume that the number of one rupee coins is 2x, the number of 50 paise coins is 3x, and the number of 25 paise coins is 4x. The total value of the coins is given as Rs.216.
The value of one rupee coins is 2x * 1 = 2x.
The value of 50 paise coins is 3x * 0.50 = 1.5x.
The value of 25 paise coins is 4x * 0.25 = x.
So, the equation becomes 2x + 1.5x + x = 216.
Simplifying the equation, we get 4.5x = 216.
Dividing both sides by 4.5, we get x = 48.
Therefore, the number of 50 paise coins is 3x = 3 * 48 = 144.

Explanation

Let's assume that the number of one rupee coins is 2x, the number of 50 paise coins is 3x, and the number of 25 paise coins is 4x. The total value of the coins is given as Rs.216.
The value of one rupee coins is 2x * 1 = 2x.
The value of 50 paise coins is 3x * 0.50 = 1.5x.
The value of 25 paise coins is 4x * 0.25 = x.
So, the equation becomes 2x + 1.5x + x = 216.
Simplifying the equation, we get 4.5x = 216.
Dividing both sides by 4.5, we get x = 48.
Therefore, the number of 50 paise coins is 3x = 3 * 48 = 144.

99. Milk and water are mixed in vessel A in the proportion 5 : 2 and in vessel B in the proportion 8 : 5 in what proportion should quantities be taken from the two vessels so as to from a mixture in which milk & water be in the proportion of 9:4

7:2

2:7

1:4

5:1

To form a mixture in which milk and water are in the proportion of 9:4, quantities should be taken from the two vessels in the proportion of 7:2.

Explanation

To form a mixture in which milk and water are in the proportion of 9:4, quantities should be taken from the two vessels in the proportion of 7:2.

100. $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»5«/mn»«/mfrac»«mo»:«/mo»«mfrac»«mn»1«/mn»«mi»x«/mi»«/mfrac»«/math»$ = $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mi»x«/mi»«/mfrac»«mo»:«/mo»«mfrac»«mn»1«/mn»«mn»125«/mn»«/mfrac»«/math»$ then the value of x is :

21

23

25

35

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Explanation

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101. The compound ratio of a:x and y:b is

Ab : xy

Xb : ay

Ay : xb

Xy: ab

The compound ratio of a:x and y:b is ay : xb. This means that the ratio of a to x is the same as the ratio of y to b. In other words, if we compare the two ratios, we can see that the first term of the first ratio (a) is related to the second term of the second ratio (xb), and the second term of the first ratio (x) is related to the first term of the second ratio (ay). Therefore, the correct answer is ay : xb.

Explanation

The compound ratio of a:x and y:b is ay : xb. This means that the ratio of a to x is the same as the ratio of y to b. In other words, if we compare the two ratios, we can see that the first term of the first ratio (a) is related to the second term of the second ratio (xb), and the second term of the first ratio (x) is related to the first term of the second ratio (ay). Therefore, the correct answer is ay : xb.

102. (3x+3) : (9x+7) is the duplicate ratio of 3:5, then the value of x is:

6

2

9

10

The given expression is a ratio in the form of (3x+3) : (9x+7). The duplicate ratio of 3:5 means that the ratio can be simplified by dividing both terms by the same number. In this case, the common divisor is 3. By dividing both terms of the ratio by 3, we get (x+1) : (3x+7/3). Simplifying further, we can multiply both terms by 3 to eliminate the fraction, resulting in 3x+3 : 9x+7. Comparing this with the given expression, we can conclude that x must be equal to 2.

Explanation

The given expression is a ratio in the form of (3x+3) : (9x+7). The duplicate ratio of 3:5 means that the ratio can be simplified by dividing both terms by the same number. In this case, the common divisor is 3. By dividing both terms of the ratio by 3, we get (x+1) : (3x+7/3). Simplifying further, we can multiply both terms by 3 to eliminate the fraction, resulting in 3x+3 : 9x+7. Comparing this with the given expression, we can conclude that x must be equal to 2.

103. If one star equal four circles and three circles equal four diamonds, then the ratio of star : diamonds is :

3/16

1/3

3/4

16/3

If one star is equal to four circles and three circles are equal to four diamonds, then we can use this information to find the ratio of star to diamonds. Since one star is equal to four circles and three circles are equal to four diamonds, we can say that one star is equal to (4/3) diamonds. Therefore, the ratio of star to diamonds is 16/3.

Explanation

If one star is equal to four circles and three circles are equal to four diamonds, then we can use this information to find the ratio of star to diamonds. Since one star is equal to four circles and three circles are equal to four diamonds, we can say that one star is equal to (4/3) diamonds. Therefore, the ratio of star to diamonds is 16/3.

104. The ratio compounded of 4 : 9 and the duplicate ratio of 3 :4 is

1:3

1:4

3:1

None

The correct answer is 1:4. The ratio compounded of 4:9 means that the first number is multiplied by 4 and the second number is multiplied by 9. The duplicate ratio of 3:4 means that the first number is multiplied by 3 and the second number is multiplied by 4. Therefore, the resulting ratio is 1:4.

Explanation

The correct answer is 1:4. The ratio compounded of 4:9 means that the first number is multiplied by 4 and the second number is multiplied by 9. The duplicate ratio of 3:4 means that the first number is multiplied by 3 and the second number is multiplied by 4. Therefore, the resulting ratio is 1:4.

105. The ratio compounded of 4 : 9 the duplicate ratio of 3 :4, the triplicate ratio of 2:3 and 9:7 is:

2:7

7:2

2:21

None

The given question is asking for the ratio compounded of different ratios. The duplicate ratio of 3:4 is 6:8, the triplicate ratio of 2:3 is 6:9, and the ratio 9:7 remains the same. To find the compounded ratio, we multiply all the ratios together. Therefore, the compounded ratio is 6:8 * 6:9 * 9:7 = 2:21.

Explanation

The given question is asking for the ratio compounded of different ratios. The duplicate ratio of 3:4 is 6:8, the triplicate ratio of 2:3 is 6:9, and the ratio 9:7 remains the same. To find the compounded ratio, we multiply all the ratios together. Therefore, the compounded ratio is 6:8 * 6:9 * 9:7 = 2:21.

106. The mean proportional between 40&90is

60

6

40

9

The mean proportional between two numbers is the square root of their product. In this case, the product of 40 and 90 is 3600, and the square root of 3600 is 60. Therefore, the mean proportional between 40 and 90 is 60.

Explanation

The mean proportional between two numbers is the square root of their product. In this case, the product of 40 and 90 is 3600, and the square root of 3600 is 60. Therefore, the mean proportional between 40 and 90 is 60.

107. The ratio of the quantities is 5:7. If the consequent of its inverse ratio is 5, the antecedent is: Options : (A)5 (B) (C)7 (D)None

A

B

C

D

The given question is asking for the antecedent of the inverse ratio. Since the ratio is 5:7, the inverse ratio would be 7:5. The consequent of the inverse ratio is given as 5. Therefore, the antecedent of the inverse ratio would be 7. Therefore, the correct answer is option C.

Explanation

The given question is asking for the antecedent of the inverse ratio. Since the ratio is 5:7, the inverse ratio would be 7:5. The consequent of the inverse ratio is given as 5. Therefore, the antecedent of the inverse ratio would be 7. Therefore, the correct answer is option C.

108. Present age of Anu and Minu are in the ratio 6:5 respectively. Seven years hence this ratio will become 7:6. Find the present age of Minu.

48

42

35

25

Let's assume the present age of Anu and Minu to be 6x and 5x respectively. Seven years later, their ages will be 6x+7 and 5x+7. According to the given information, (6x+7)/(5x+7) = 7/6. Cross-multiplying and simplifying, we get 36x + 42 = 35x + 49. Solving this equation, we find x = 7. Therefore, Minu's present age is 5x = 5*7 = 35.

Explanation

Let's assume the present age of Anu and Minu to be 6x and 5x respectively. Seven years later, their ages will be 6x+7 and 5x+7. According to the given information, (6x+7)/(5x+7) = 7/6. Cross-multiplying and simplifying, we get 36x + 42 = 35x + 49. Solving this equation, we find x = 7. Therefore, Minu's present age is 5x = 5*7 = 35.

109. If 40% of a number is equal to two -third of another number, what is the ratio of first number to the second number?

2:5

3:7

5:3

7:3

To find the ratio of the first number to the second number, we need to determine the values of both numbers. Let's assume the first number is x and the second number is y. The given information states that 40% of x is equal to two-thirds of y. Mathematically, this can be expressed as 0.4x = (2/3)y. To simplify this equation, we can multiply both sides by 10 to eliminate decimals, resulting in 4x = (20/3)y. Now, to find the ratio, we divide both sides by y, giving us (4x/y) = (20/3). Simplifying further, we get x/y = (20/3) / 4, which simplifies to x/y = 5/3. Therefore, the ratio of the first number to the second number is 5:3.

Explanation

To find the ratio of the first number to the second number, we need to determine the values of both numbers. Let's assume the first number is x and the second number is y. The given information states that 40% of x is equal to two-thirds of y. Mathematically, this can be expressed as 0.4x = (2/3)y. To simplify this equation, we can multiply both sides by 10 to eliminate decimals, resulting in 4x = (20/3)y. Now, to find the ratio, we divide both sides by y, giving us (4x/y) = (20/3). Simplifying further, we get x/y = (20/3) / 4, which simplifies to x/y = 5/3. Therefore, the ratio of the first number to the second number is 5:3.