Ratios And Proportions Quiz Questions
Questions and Answers
- 1.
The triplicate ratio of 1:2 is
- A.
1:8
- B.
1:4
- C.
4 :1
- D.
8 :1
Correct Answer
A. 1:8Explanation
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.Rate this question:
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- 2.
The sub-triplicate ratio of 1:1 is
- A.
3:3
- B.
1:1
- C.
2:2
- D.
None
Correct Answer
B. 1:1Explanation
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.Rate this question:
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- 3.
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) (D)
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
A. AExplanation
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.Rate this question:
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- 4.
The duplicate ratio of : is Options : (A) b:a (B) : (C) a:b (D):
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
C. CExplanation
The correct answer is C. The duplicate ratio of a to b is represented as a:b.Rate this question:
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- 5.
The sub-triplicate ratio of y3: w3 is Options : (A) y2:w2 (B) w:y (C) w2: y2 (D) y: w
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
D. DExplanation
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.Rate this question:
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- 6.
If a, b, c, d are said to be in proportion then
- A.
Ad = bc
- B.
Ac = bd
- C.
Ad not equal bc
- D.
Ac not equal bd
Correct Answer
A. Ad = bcExplanation
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.Rate this question:
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- 7.
The compound ratio of a:x and y:b is
- A.
Ab : xy
- B.
Xb : ay
- C.
Ay : xb
- D.
Xy: ab
Correct Answer
C. Ay : xbExplanation
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.Rate this question:
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- 8.
The compound ratio of (x - y): (x2 - y2) and (x+y): 1 is
- A.
(x-y):(x+y)
- B.
X:y
- C.
Y:x
- D.
1:1
Correct Answer
D. 1:1Explanation
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.Rate this question:
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- 9.
The triplicate ratio of : Options: (A) b: a (B) a : b (C) a3: b3 (D) b3 : a3
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
B. BExplanation
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.Rate this question:
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- 10.
If a,b,c are in continued proportion then Options : (A) : ac (B) a: b (C) = ab (D) ac not equal to bd
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
A. AExplanation
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.Rate this question:
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- 11.
The mean proportional between 279 and 31 is
- A.
39
- B.
93
- C.
91
- D.
L9
Correct Answer
B. 93Explanation
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.Rate this question:
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- 12.
The third proportional between 2 & 7 is
- A.
49/2
- B.
49
- C.
2
- D.
7
Correct Answer
A. 49/2Explanation
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.Rate this question:
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- 13.
The fourth proportional to the number 40,14,20 is
- A.
14
- B.
7
- C.
15
- D.
28
Correct Answer
B. 7Explanation
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.Rate this question:
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- 14.
Find the number, in which when subtracted from each numbers 17, 8, 7, 4 will make them in proportional
- A.
1
- B.
3
- C.
2
- D.
5
Correct Answer
C. 2Explanation
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.Rate this question:
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- 15.
The fourth proportional to 3a, 5b & 6c is Options : (A) (B) 10bc (C) a (D)
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
A. AExplanation
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.Rate this question:
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- 16.
The mean proportional between 1.4 grains and 5.6 grams is
- A.
28 gms
- B.
2.8gms
- C.
3.2gms
- D.
None
Correct Answer
B. 2.8gmsExplanation
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.Rate this question:
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- 17.
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.
A
- B.
B
- C.
C
- D.
D
Correct Answer
D. DExplanation
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.Rate this question:
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- 18.
What is the value of if =5
- A.
2/3
- B.
3/2
- C.
2/6
- D.
4/3
Correct Answer
B. 3/2 -
- 19.
The mean proportional between 40&90is
- A.
60
- B.
6
- C.
40
- D.
9
Correct Answer
A. 60Explanation
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.Rate this question:
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- 20.
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.
A
- B.
B
- C.
C
- D.
D
Correct Answer
B. BExplanation
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.Rate this question:
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- 21.
If when then the process is called
- A.
Invertendo
- B.
Alternendo
- C.
Componendo and dividendo
- D.
None
Correct Answer
C. Componendo and dividendoExplanation
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.Rate this question:
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- 22.
If 5 : 7 = x: 28 then x is
- A.
20
- B.
28
- C.
35
- D.
7
Correct Answer
A. 20Explanation
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.Rate this question:
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- 23.
If then is
- A.
9
- B.
4
- C.
5
- D.
3
Correct Answer
D. 3 -
- 24.
The ratio between consonants and alphabets is
- A.
5/21
- B.
21/26
- C.
5/21
- D.
5/26
Correct Answer
B. 21/26Explanation
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.Rate this question:
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- 25.
The mean proportionalbetween 12a2b2 and 27b2c2 Options: (A) 18a2b2c2 (B) 18abc (C) 18ab2c (D) 18a2bc
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
C. CExplanation
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.Rate this question:
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- 26.
The four numbers are proportional ,then x is
- A.
Bc/a
- B.
Ac/b
- C.
Ab/c
- D.
Abc
Correct Answer
A. Bc/aExplanation
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.Rate this question:
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- 27.
The mean proportional between 1.44 and 6.25is
- A.
25
- B.
12
- C.
9
- D.
3
Correct Answer
D. 3Explanation
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.Rate this question:
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- 28.
What must be subtracted from each of the numbers 21, 38, 55, 106 so that they becomes in proportional
- A.
2
- B.
3
- C.
4
- D.
5
Correct Answer
C. 4Explanation
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.Rate this question:
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- 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
- A.
Rs.3400
- B.
Rs.3600
- C.
Rs.4000
- D.
Rs.4400
Correct Answer
C. Rs.4000Explanation
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.Rate this question:
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- 30.
If A = then A:B:C is
- A.
2:3:4
- B.
2:3:5
- C.
1:2:5
- D.
1:2:3
Correct Answer
C. 1:2:5Explanation
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.Rate this question:
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- 31.
If a:b = 3:4 the value of (2a+3b): (3a+4b)
- A.
18:25
- B.
8:25
- C.
17:24
- D.
24:17
Correct Answer
A. 18:25Explanation
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.Rate this question:
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- 32.
The compound ratio of two ratios 4 : 5 & 7: 5is
- A.
25 :28
- B.
20 :35
- C.
28 :25
- D.
35 :20
Correct Answer
C. 28 :25Explanation
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.Rate this question:
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- 33.
If p : q = r : s, implies q : p = s : r then the process is called
- A.
Componendo
- B.
Invertendo
- C.
Alternendo
- D.
Dividendo
Correct Answer
B. InvertendoExplanation
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.Rate this question:
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- 34.
If p : q is the sub-duplicate ratio of p-x2: q-x2 then x2 is Options : (A) (B) (C) (D)
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
B. BExplanation
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.Rate this question:
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- 35.
Find the value of x if
- A.
15/2
- B.
2/15
- C.
3/4
- D.
9/10
Correct Answer
B. 2/15Explanation
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.Rate this question:
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- 36.
If then
- A.
8
- B.
5
- C.
4
- D.
None
Correct Answer
D. None -
- 37.
Division of Rs.1100 into 3 parts in the ratio of 4:5:6, the numbers are:
- A.
293.33,25,15
- B.
293.33,366.67,440
- C.
400,300,400
- D.
200,500,400
Correct Answer
B. 293.33,366.67,440 -
- 38.
The ratio between days of non-leap year and leap year is
- A.
366 : 365
- B.
365:366
- C.
1:365
- D.
31:30
Correct Answer
B. 365:366Explanation
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.Rate this question:
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- 39.
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?
- A.
9
- B.
25
- C.
10
- D.
15
Correct Answer
C. 10Explanation
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.Rate this question:
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- 40.
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.
- A.
75yrs
- B.
25yrs
- C.
50yrs
- D.
None
Correct Answer
A. 75yrsExplanation
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.Rate this question:
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- 41.
If 40% of a number is equal to two -third of another number, what is the ratio of first number to the second number?
- A.
2:5
- B.
3:7
- C.
5:3
- D.
7:3
Correct Answer
C. 5:3Explanation
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.Rate this question:
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- 42.
If 9: x = x : 4 then x is equal to
- A.
9
- B.
6
- C.
36
- D.
48
Correct Answer
B. 6Explanation
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.Rate this question:
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- 43.
The fourth proportional of 0.2, 0.12 and 0.3 is
- A.
0.18
- B.
1.12
- C.
1.20
- D.
1.32
Correct Answer
A. 0.18Explanation
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.Rate this question:
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- 44.
Find the third proportional to the numbers 4 and 42
- A.
541
- B.
441
- C.
641
- D.
540
Correct Answer
B. 441Explanation
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.Rate this question:
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- 45.
If 0.75 : x = 5 :8 then x is equal to
- A.
1.20
- B.
1.25
- C.
1.12
- D.
1.30
Correct Answer
A. 1.20Explanation
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.Rate this question:
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- 46.
The sub-duplicate ratio of 324 : 361 is Options: (A) 18x: 19y (B) 18x2:19y3 (C) 19y3:18x (D) 19:18
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
B. B -
- 47.
The triplicate ratio of 3 :2 is
- A.
27:8
- B.
6:9
- C.
3:2
- D.
None of these
Correct Answer
A. 27:8Explanation
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.Rate this question:
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- 48.
If A : C = :and C : B = 0.85 : 0.1 then find A: B
- A.
493:76
- B.
76:493
- C.
4.93:7.6
- D.
49.3:0.76
Correct Answer
A. 493:76Explanation
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.Rate this question:
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- 49.
If 2s : 3t is the duplicate ratio of 2s - p: 3t - p, then
- A.
P2 = 6st
- B.
P = 6st
- C.
2p = 3st
- D.
None of these
Correct Answer
A. P2 = 6stExplanation
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.Rate this question:
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- 50.
= then the value of x is :
- A.
21
- B.
23
- C.
25
- D.
35
Correct Answer
C. 25 -
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