1. If [latex]({4x}^{2} - {5y}^{2}) : ({2x}^{2} + {5y}^{2})[/latex] = 12 : 19, then x : y is

A. 2 : 3 B. 1 : 2 C. 3 : 2 D. 2 : 1

Answer - Option C
2. If [latex]\frac{x}{5} = \frac{x}{8}[/latex], then (x+ 5) : (y + 8) is equal to

A. 3 : 5 B. 13 : 8 C. 8 : 5 D. 5 : 8

Answer - Option D
3. If x : y = 6 : 5, then ( 5x + 3y) : ( 5x – 3y) is equal to

A. 2 : 1 B. 3 : 1 C. 5 : 3 D. 5 : 2

Answer - Option B
4. What same number must be added to each term of the ratio 7 : 3 so that the ratio becomes 2 : 3

A. 1 B. 2 C. 5 D. Can’t be determined

Answer - Option D
5. The ratio of the two numbers is 3 : 4 & their sum is 420. The greater of the two numbers is

A. 175 B. 200 C. 240 D. 315

Answer - Option C
6. Five bananas and four apples cost as much as three bananas and seven apples. The ratio of the cost of one banana to that of one apple is

A. 3 : 2 B. 4 : 3 C. 3 : 4 D. 1 : 3

Answer - Option A
7. The speeds of three cars are in the ratio 5 : 4 : 6. The ratio between the times taken by them to travel the same distance is

A. 5 : 4 : 6 B. 6 : 4 : 5 C. 10 : 12 : 15 D. 12 : 15 : 10

Answer - Option D
8. A dog takes 3 leaps for every 5 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is

A. 8 : 5 B. 9 : 5 C. 8 : 7 D. 9 : 7

Answer - Option B
9. Rs 180 contained in a box consists of one rupee, 50 paise and 25 paise coins in the proportion of 2 : 3 : 4. What is the number of 50 paise coins?

A. 120 B. 150 C. 180 D. 240

Answer - Option A
10. In a school, 10% of the boys are same in number as[latex]\frac{1}{4}[/latex] of the girls and 10% of the girls are same in number as 1/25 of the boys. What is the ratio of boys to girls in that school

A. 3 : 2 B. 5 : 2 C. 2 : 1 D. 4 : 3

Answer - Option B
11. Two numbers are in the ratio 3 : 4 and the product of their L.C.M. & H.C.F is 10800. The sum of the numbers is

A. 180 B. 210 C. 225 D. 240

Answer - Option B
12. The ages of x and y are in the ratio of 3 : 1. After 15 years the ratio will be 2 : 1. Their present ages(in years) are

A. 30, 10 B. 45, 15 C. 21, 7 D. 60, 20

Answer - Option B
13. Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should there be mixed to get an alloy 15 times as heavy as water

A. 1 : 1 B. 2 : 3 C. 1 : 2 D. 3 : 2

Answer - Option D
14. 85 liters of a mixture contains milk and water in the ratio 27 : 7. How much more water is to be added to get a new mixture containing milk and water in the ratio 3 : 1?

A. 5 lt. B. 6.5 lt C. 7.25 lt. D. 8 lt.

Answer - Option A

1. Sachin is younger than Rahul by 4 years. If their ages are in the ratio of 7 ; 9, then how old is Sachin?

A. 14 years B. 21 years C. 18 years D. 25 years

Answer - Option A
Explanation -
S : R = 7X : 9x
9x – 7x = 4
or x = 2
Hence, S or age of Sachin = 7 × 2 = 14 years.
2. The sum of two numbers is 40 and the difference of these two numbers is 4. Find the ratio of these two numbers.

A. 11 : 9 B. 11 : 18 C. 22 : 9 D. 17 : 13

Answer - Option A
Explanation -
a +b = 40 and a – b = 4
a = 22 and b = 18
Hence, a : b = 11 : 9
3. If A exceeds B by 40% and B is less than C by 20%. then A : C = ?

A. 3 : 1 B. 3 : 2 C. 26 : 25 D. 28 : 25

Answer - Option D
Explanation -
Let C = 100, such that B = 80 and
A = 80 * 1.4 = 112
Hence, A : C = 112 : 100 = 28 : 25
4. If a : b = 3 : 5 and b : c = 2 : 3, then a : c is

A. 3 : 2 B. 2 : 5 C. 5 : 2 D. 5 : 8

Answer - Option B
Explanation -
Given: a : b = 3 : 5 and b : c = 2 : 3
a : b = 6 : 10 and b : c = 10 : 15
(making the value of ‘b’ equal in both the ratios)
a : c = 6 : 15 = 2 : 5.
5. Which of the following numbers are in proportion

A. 12, 27, 54, 24 B. 27, 12, 24, 54 C. 12, 27, 24, 54 D. 54, 24, 12, 27

Answer - Option C
Explanation -
Among the given options only 12, 27, 24 and 54 are in proportion i.e. 12 : 27 = 24 : 54 = 4 : 9.
6. In two vessels A and B, milk and water are in the ratio of 4 : 3 and 3 : 5 respectively. The ratio in which these are to be mixed to obtain new mixture which contains half milk and half water

A. 7 : 4 B. 7 : 8 C. 1 : 2 D. 4 : 5

Answer - Option A
Explanation -
Applying allegation for milk we get:

Hence, required ratio = [latex]\frac{1}{8}[/latex] : [latex]\frac{1}{14}[/latex] = 7 : 4
7. If a : b = 4: 5 and b : c = 2 : 3, then c : a is

A. 15 : 8 B. 5 : 4 C. 8 : 15 D. 5 : 8

Answer - Option C
Explanation -
a : b = 4 : 5 and b : c = 2 : 3
a : b = 8 : 10 and b : c = 10 : 15
c : a = 15 : 8
8. If a : b = 5 : 6 and b : c = 3 : 4, then c : a is

A. 4 : 5 B. 5 : 4 C. 8 : 5 D. 5 : 8

Answer - Option C
Explanation -
a : b = 5 : 6; b : c = 3 : 4
= 15 : 18 = 15 : 20
= 18 : 24
i.e, c : a = 24 : 15
= 8 : 5
9. If a : b = 2 : 3 and a + b = 45. then a is equal to

A. 27 B. 25 C. 18 D. 9

Answer - Option C
Explanation -
[latex]\frac{a}{b}[/latex] = [latex]\frac{2}{3} a + b[/latex] = 45
a : b = 2x : 3x
5x = 45
a = 2x = 18
10. If 2, x, [latex]{x}^{2}[/latex], 4 are in proportion, then x is equal to

A. 2 B. 4 C. 8 D. 16

Answer - Option A
Explanation -
2, x, [latex]{x}^{2}[/latex]x2, 4 are in proportion
[latex]{2x}^{2}[/latex] = x × 4
x = 2
11. In two vessels A and B, spirit and water are in the ratio 2 : 1 and 2 : 3 respectively. The ratio in which these ire mixed which contains half water

A. 5 : 3 B. 3 : 5 C. 2 : 3 D. 3 : 2

Answer - Option B
Explanation -
i.e, ratio = [latex]{1}^{10}[/latex] = [latex]{1}^{6}[/latex]
= 6 : 10 = 3 : 5
12. The average of 20 observations is 18 and average of 30 observations is 25. The average of all 50 observations is

A. 21.5 B. 21.8 C. 22.2 D. 22.5

Answer - Option C
Explanation -
Average = [latex]\frac{20 * 18 * 30 * 25}{50}[/latex] = 22.2
13. If 4, x, 2x, 32 are in proportion, then x is equal to

A. 8 [latex]\sqrt{2}[/latex] B. 8 C. 16 D. 16 [latex]\sqrt{2}[/latex]

Answer - Option B
Explanation -
4, x, 2x, 32 are in propertion
Product of extremes = product pf weavs
4 × 32 = 2x × x
x = 8
14. If 8, 3x, 6, 27 are in proportion, then x is equal to

A. 6 B. 9 C. 12 D. 15

Answer - Option C
Explanation -
Product of means = product of extremes
3x × 6 = 8 × 27
x = 12
15. In two vessels A and B, the milk and water are in the ratio 5 : 4 and 3 : 5 respectively. The ratio in which these are mixed to obtain new mixture which Contains half milk and half water is

A. 9 : 4 B. 4 : 9 C. 4 : 3 D. 3 : 4

Answer - Option A
Explanation -
Let quantity of liquid of A m mixture = x Let _____ B _____ = y
i.e, Milk from A + Milk from B = total milk
[latex]x\frac{5}{9} + y\frac{3}{8} = (x + y) \frac{1}{2}[/latex]
[latex]\frac{x}{y} = \frac{9}{4}[/latex] = 9 : 4

1. If a : b = 4 : 3 and b : c = 7 : 9, then a : b : c : ?

A. 24 : 21 : 30 B. 12 : 15 : 21 C. 8 : 6 : 12 D. 28 : 2l : 27

Answer - Option D
Explanation -
a : b = 4 : (3)* 7 = 4 *3 = 4 * 7 : 3 * 7
b : c 7 : (9)* 3 and 7 : 9 = 7 * 3 : 9 *3
a : b = 28 : 21
b : c = 21 : 27
i.e, a : b : c = 28 : 21 : 27
2. Ravi spends [latex]\frac{2}{5}[/latex] of his salary on House Rent; [latex]\frac{3}{10}[/latex] of his salary on Food and [latex]\frac{1}{8}[/latex] of his Salary on Conveyance. After this, he is left with Rs. 1400. Find his expenditure on Food

A. Rs. 8000 B. Rs. 3200 C. Rs. 2400 D. Rs. 1000

Answer - Option C
Explanation -
Let the salary of Ravi be Rs. x
Total expenditure = [latex]x \frac{2}{5}[/latex] + [latex]x \frac{3}{10}[/latex] + [latex]x \frac{1}{8}[/latex] = [latex]x \frac{33}{40}[/latex]
Money left = 1 - [latex]x \frac{33}{40} = x \frac{7}{40}[/latex] = 1400
x = 8000
i.e, Money spent on food
= [latex] \frac{3}{10}[/latex]* 8000 = 2400
3. A sum of Rs. 312 was divided among 60 boys and some girls in such a way that each boy gets Rs.3.60 and each girl Rs. 2.40. The number of girls is

A. 35 B. 40 C. 60 D. 65

Answer - Option B
Explanation -
No. of girls
[latex]\frac{3{\frac {3}{2}} - 60 * 3.6}{2.4}[/latex] = 40
4. Some students planned a trip. The budget for food was Rs. 500 But, 5 of them failed to go and thus the cost of food for each member increased by Rs.5. How many students attended the trip ?

A. 15 B. 20 C. 25 D. 30

Answer - Option B
Explanation -
Let the no. of students initially = x
According to question [latex]\frac{\frac{500}{x - 5}}{\frac {500}{x}}[/latex] = 5
x = 25
No. of students who attended the trip = x – 5 = 20
5. In a class, there are two sections A and B. I f 10 students of section B shift over to section A, the strength of A becomes three times the strength of B. But, if 10 students shift over from A to B, both A and B are equal in strength. How many students are there in sections A and B ?

A. 50 and 30 B. 45 and 15 C. 90 and 40 D. 80 and 40

Answer - Option A
Explanation -
Let the no. of students in class A = x
Let the no. of students in class B = y
According to question
(x + 10) = 3(y – 10) … (i)
also (x – 10) = y + 10 … (ii)
Solving eq. (i) and (ii), we get
x = 50 and y = 30
6. Six persons went to a hotel for meals. Five of them spent Rs. 32 each on their meals while the [latex]{6}^{th}[/latex] person spent Rs. 80 more than the average expenditure of all the six. Total money spent by all the persons is :

A. Rs. 192 B. Rs. 240 C. Rs. 288 D. Rs. 336

Answer - Option C
Explanation -
Let avg expenditure be x.
i.e, x = [latex]\frac{32 * 5 + (80 + 2)}{6}[/latex]
x = 48
i.e, Total money spent = (32 × 5) + (80 + 48)
= 288
7. X is 40 years old and Y is 60 years old How many years ago was the ratio of their ages 3:5

A. 5 years B. 10 years C. 20 years D. 37 years

Answer - Option B
Explanation -
According to question,
[latex]\frac{40 - k}{60 - k}[/latex] = [latex]\frac{3}{5}[/latex]
k = 10 years
8. Rs. 680 is divided among A, B, C such that A gets [latex]\frac{2}{3}[/latex] of what B gets and B gets [latex]\frac{1}{4}[/latex] of what C gets. Then their shares are respectively

A. Rs. 75, Rs. 325, Rs. 280 B. Rs. 80, Rs. 120, Rs. 480 C. Rs. 90, Rs. 210, Rs. 380 D. Rs. 100, Rs. 200, Rs. 380

Answer - Option B
Explanation -
According to question,
[latex]A = \frac{2B}{3}[/latex]
[latex]B =\frac{3A}{2}[/latex]
and [latex]B = \frac{1C}{4}[/latex]
C = 4B = 4[latex]\frac{3A}{2}[/latex]
C = 6A
Now A + B + C = 680
A + [latex]\frac{3A}{2}[/latex]+ 6A = 680
i.e, A = 80
i.e, B = 120
i.e, C = 480
9. X. Y and Z start a business X invests 3 times as much as Y invests and Y invests [latex]\frac{2}{3}[/latex]rd of what Z invests. Then the ratio of capitals of X. Y, Z is 3

A. 3 : 9 : 2 B. 6 : 10 : 15 C. 5 : 3 : 2 D. 6 : 2 : 3

Answer - Option D
Explanation -
According to question, x = 3y
x : y = [latex]\frac{3}{1} * \frac{2}{2} * \frac{6}{2}[/latex]
y = [latex] z \frac{2}{3}[/latex]
y : x = 2 : 3
x : y = 6 : 2
x : y : z = 6 : 2 : 3
10. Entry fee to an exhibition was Rs.80. Later, this was reduced by 25% which increased the sale by 20%. The percentage increased in the number of visitors is

A. 30 B. 40 C. 60 D. 80

Answer - Option C
Explanation -
Entry fee × No. of visitors = sales.
Multiplying factor = [latex]\frac{3}{4} * x = \frac{6}{5}[/latex]
x = [latex]\frac{8}{5}[/latex] = 1 + [latex]\frac{3}{5}[/latex] = increase of [latex]\frac{3}{5}[/latex] in no. of persons
60 % increase
11. If a : b = 8 : 15 , b : c = 5 : 8 and c : d = 4 : 5, then b : d is

A. 1 : 2 B. 1 : 3 C. 4 : 15 D. 5 : 8

Answer - Option A
Explanation -
[latex]\frac{a}{b}[/latex] = [latex]\frac{8}{15}[/latex];[latex]\frac{b}{c}[/latex] = [latex]\frac{5}{8}[/latex];[latex]\frac{c}{d}[/latex] = [latex]\frac{4}{5}[/latex];
[latex]\frac{a}{b}[/latex] * [latex]\frac{c}{d}[/latex] = [latex]\frac{8}{15}[/latex] * [latex]\frac{4}{5}[/latex] = [latex]\frac{1}{2}[/latex]
12. A person gave [latex]\frac{1}{5}[/latex] part his income to his son and 40 % part of his income to his daughter. He lent out the remaining money in three trusts A, B and C in the ratio of 5 : 3 : 2. I f the difference between the amount got by son and daughter is Rs. 50,000, how much amount did he invest in trust B?

A. Rs. 20000 B. Rs. 30000 C. Rs. 40000 D. Rs. 50000

Answer - Option B
Explanation -
Amount received by son = 20%
Amount received by daughter = 40%
Amount given to trust = 40 %
Difference = 20% is Rs. 50,000
40% = Rs. 1,00,000.
A : B : C = 5 : 3 : 2
B gets [latex]\frac{3}{10}[/latex] * 1,00,000 = Rs. 30,000
13. Two alloys A and B contain zinc and copper in the ratio 5 : 6 and 7 : 8 respectively. If equal quantities of alloys are melted to form a third alloys C, then the ratio of copper and zinc in C will be

A. 76 : 89 B. 89 : 76 C. 48 : 35 D. 35 : 48

Answer - Option B
Explanation -
Let quantity of alloy A = x
Let quantity of alloy B = y
Zinc in alloy (A + B) = [latex]\frac{5x}{11}[/latex] + [latex]\frac{7y}{15}[/latex]
copper in alloy (A + B) = [latex]\frac{6x}{11}[/latex] + [latex]\frac{8x}{15}[/latex]
[latex]\frac{Copper in C}{Zinc in C}[/latex] = [latex]\frac{\frac{6x}11{} + \frac{8x}{15}}{\frac{5x}{11} + \frac{7y}{15}}[/latex] = [latex]\frac{89}{76}[/latex]
i.,e x = y (quantities are same)
14. If A : B = 2 : 3, B : C = 5 : 6 and C : D 8 : 9, then A : D is

A. 2 : 9 B. 20 : 81 C. 20 : 27 D. 40 : 81

Answer - Option D
Explanation -
[latex]\frac{A}{B}[/latex] = [latex]\frac{2}{3}[/latex],[latex]\frac{B}{C}[/latex] = [latex]\frac{5}{6}[/latex], [latex]\frac{C}{D}[/latex] = [latex]\frac{8}{9}[/latex]
[latex]\frac{A}{B}[/latex] * [latex]\frac{B}{C}[/latex] * [latex]\frac{C}{D}[/latex] = [latex]\frac{2}{3}[/latex] * [latex]\frac{5}{6}[/latex] * [latex]\frac{8}{9}[/latex]
[latex]\frac{A}{D}[/latex] = [latex]\frac{40}{81}[/latex]
15. A sum of Rs.16500 is to be divided among A, B, C and D in such a way that the ratio of shares of A and B is 3:4, that of B and C is 1:3 and that of C and D is 6:7. Sum of shares of A and D is

A. Rs.8000 B. Rs.7500 C. Rs.8500 D. Rs.9000

Answer - Option C
Explanation -
A : B : C = 3 : 4 : 12
C : D = 12 : 14
A : B : C : D = 3 : 4 : 12 : 14
sum of shares of A and D is [latex]\frac{3 + 14}{33}* 16500[/latex] = 8500