1.
The triplicate ratio of 1:2 is
Correct Answer
A. 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.
2.
The sub-triplicate ratio of 1:1 is
Correct Answer
B. 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.
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)
Correct Answer
A. A
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.
4.
The duplicate ratio of : is
Options :
(A) b:a
(B) :
(C) a:b
(D):
Correct Answer
C. C
Explanation
The correct answer is C. The duplicate ratio of a to b is represented as a:b.
5.
The sub-triplicate ratio of y^{3}: w^{3} is
Options :
(A) y^{2}:w^{2}
(B) w:y
(C) w^{2}: y^{2}
(D) y: w
Correct Answer
D. D
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.
6.
If a, b, c, d are said to be in proportion then
Correct Answer
A. Ad = bc
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.
7.
The compound ratio of a:x and y:b is
Correct Answer
C. 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.
8.
The compound ratio of (x - y): (x^{2} - y^{2}) and (x+y): 1 is
Correct Answer
D. 1:1
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.
9.
The triplicate ratio of :
Options:
(A) b: a
(B) a : b
(C) a^{3}: b^{3}
(D) b^{3} : a^{3}
Correct Answer
B. B
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.
10.
If a,b,c are in continued proportion then
Options :
(A) : ac
(B) a: b
(C) = ab
(D) ac not equal to bd
Correct Answer
A. A
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.
11.
The mean proportional between 279 and 31 is
Correct Answer
B. 93
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.
12.
The third proportional between 2 & 7 is
Correct Answer
A. 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.
13.
The fourth proportional to the number 40,14,20 is
Correct Answer
B. 7
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.
14.
Find the number, in which when subtracted from each numbers 17, 8, 7, 4 will make them in proportional
Correct Answer
C. 2
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.
15.
The fourth proportional to 3a, 5b & 6c is
Options :
(A)
(B) 10bc
(C) a
(D)
Correct Answer
A. 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.
16.
The mean proportional between 1.4 grains and 5.6 grams is
Correct Answer
B. 2.8gms
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.
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) a^{2}: b^{2}
(B) a: b = a^{2}: c^{2}
(C) b^{2}: c^{2}
(D) a : c = a^{2}: b^{2}
Correct Answer
D. D
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.
18.
What is the value of if =5
Correct Answer
B. 3/2
19.
The mean proportional between 40&90is
Correct Answer
A. 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.
20.
The fourth proportional between (x+y), (x+y)^{2}, (x-y) is
Options :
(A) (x + y)
(B) x^{2}-y^{2}
(C) (x-y)
(D) (x+y)^{2}
Correct Answer
B. B
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.
21.
If when then the process is called
Correct Answer
C. Componendo and dividendo
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.
22.
If 5 : 7 = x: 28 then x is
Correct Answer
A. 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.
23.
If then is
Correct Answer
D. 3
24.
The ratio between consonants and alphabets is
Correct Answer
B. 21/26
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.
25.
The mean proportionalbetween 12a^{2}b^{2 }and 27b^{2}c^{2}
Options:
(A) 18a^{2}b^{2}c^{2}
(B) 18abc
(C) 18ab^{2}c
(D) 18a^{2}bc
Correct Answer
C. 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.
26.
The four numbers are proportional ,then x is
Correct Answer
A. 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.
27.
The mean proportional between 1.44 and 6.25is
Correct Answer
D. 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.
28.
What must be subtracted from each of the numbers 21, 38, 55, 106 so that they becomes in proportional
Correct Answer
C. 4
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.
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
Correct Answer
C. 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 = then A:B:C is
Correct Answer
C. 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.
If a:b = 3:4 the value of (2a+3b): (3a+4b)
Correct Answer
A. 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.
32.
The compound ratio of two ratios 4 : 5 & 7: 5is
Correct Answer
C. 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.
33.
If p : q = r : s, implies q : p = s : r then the process is called
Correct Answer
B. Invertendo
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.
34.
If p : q is the sub-duplicate ratio of p-x^{2}: q-x^{2} then x^{2} is
Options :
(A)
(B)
(C)
(D)
Correct Answer
B. 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.
35.
Find the value of x if
Correct Answer
B. 2/15
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.
36.
If then
Correct Answer
D. None
37.
Division of Rs.1100 into 3 parts in the ratio of 4:5:6, the numbers are:
Correct Answer
B. 293.33,366.67,440
38.
The ratio between days of non-leap year and leap year is
Correct Answer
B. 365:366
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.
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?
Correct Answer
C. 10
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.
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.
Correct Answer
A. 75yrs
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.
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?
Correct Answer
C. 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.
42.
If 9: x = x : 4 then x is equal to
Correct Answer
B. 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.
43.
The fourth proportional of 0.2, 0.12 and 0.3 is
Correct Answer
A. 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.
44.
Find the third proportional to the numbers 4 and 42
Correct Answer
B. 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.
45.
If 0.75 : x = 5 :8 then x is equal to
Correct Answer
A. 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.
46.
The sub-duplicate ratio of 324 : 361 is
Options:
(A) 18x: 19y
(B) 18x^{2}:19y^{3}
(C) 19y^{3}:18x
(D) 19:18
Correct Answer
B. B
47.
The triplicate ratio of 3 :2 is
Correct Answer
A. 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.
48.
If A : C = :and C : B = 0.85 : 0.1 then find A: B
Correct Answer
A. 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.
49.
If 2s : 3t is the duplicate ratio of 2s - p: 3t - p, then
Correct Answer
A. 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.
50.
= then the value of x is :
Correct Answer
C. 25