Ratio and Proportion problems are key components of quantitative aptitude tests. They involve comparing two quantities by division and determining how one quantity is related to another. A ratio is an expression that compares quantities relative to each other, while a proportion states that two ratios are equal. These concepts are widely used in solving problems related to real-life scenarios, business, finance, and science.

## 1. The ratio of the number of boys to girls in a class is 3:4. If there are 18 boys, how many girls are there?

a) 20

b) 22

c) 24

d) 26

### Answer:

c) 24

### Explanation:

```
Number of girls = (4/3) × 18 = 24.
```

## 2. Two numbers are in the ratio 5:6. If their sum is 55, find the numbers.

a) 25 and 30

b) 20 and 35

c) 15 and 40

d) 10 and 45

### Answer:

a) 25 and 30

### Explanation:

```
Let the numbers be 5x and 6x.
Then, 5x + 6x = 55, 11x = 55, x = 5.
The numbers are 25 and 30.
```

## 3. In a mixture of 45 litres, the ratio of milk to water is 4:1. How much more water should be added to make the ratio 2:3?

a) 15 litres

b) 20 litres

c) 25 litres

d) 30 litres

### Answer:

d) 30 litres

### Explanation:

```
Quantity of milk in the mixture = (4/5) × 45 = 36 litres.
The initial quantity of water = 45 - 36 = 9 litres.
Let the amount of water to be added be x litres.
New ratio of milk to water = 36:(9 + x).
To make this ratio 2:3, 36/(9 + x) = 2/3.
Solving for x gives x = 30 litres. So, 30 litres of water should be added.
```

## 4. Divide $1200 in the ratio 3:2:5.

a) $360, $240, $600

b) $450, $300, $450

c) $480, $320, $400

d) $360, $480, $360

### Answer:

a) $360, $240, $600

### Explanation:

```
Total ratio = 3 + 2 + 5 = 10.
Shares are $1200 × (3/10) = $360, $1200 × (2/10) = $240, $1200 × (5/10) = $600.
```

## 5. The incomes of A and B are in the ratio 3:4 and their expenditures are in the ratio 4:5. If each saves $2000, find A’s income.

a) $6000

b) $8000

c) $10000

d) $12000

### Answer:

b) $8000

### Explanation:

```
Let A's income be 3x and B's income be 4x. A's expenditure = 4y, B's expenditure = 5y.
3x - 4y = 2000 and 4x - 5y = 2000. Solving gives A's income = 3x = $8000.
```

## 6. A bag contains coins of denominations $1, $2 and $5 in the ratio 3:2:1. If the total amount is $96, find the number of $2 coins.

a) 12

b) 16

c) 20

d) 24

### Answer:

b) 16

### Explanation:

```
Let the number of $1, $2, and $5 coins be 3x, 2x, and x respectively.
Total amount = 3x(1) + 2x(2) + x(5) = $96.
Solving for x gives x = 8. Number of $2 coins = 2x = 16.
```

## 7. The ratio of two numbers is 3:5 and their difference is 40. Find the numbers.

a) 60 and 100

b) 45 and 75

c) 72 and 120

d) 54 and 90

### Answer:

c) 72 and 120

### Explanation:

```
Let the numbers be 3x and 5x.
Then, 5x - 3x = 40, 2x = 40, x = 20.
The numbers are 60 and 100.
```

## 8. A container has a mixture of two liquids A and B in the ratio 7:5. When 9 litres of the mixture is drawn off and replaced with liquid B, the ratio becomes 7:9. Find the initial quantity of the mixture.

a) 45 litres

b) 54 litres

c) 63 litres

d) 72 litres

### Answer:

c) 63 litres

### Explanation:

```
Let the initial quantity be x litres.
Quantity of A in the mixture left = 7x/12 - 7(9/x) litres.
New ratio = (7x/12 - 7(9/x)):(5x/12 + 9) = 7:9.
Solving gives x = 63 litres.
```

## 9. In what ratio must a grocer mix two types of rice costing $15/kg and $20/kg so that by selling the mixture at $18/kg he gains 20%?

a) 1:2

b) 2:1

c) 3:2

d) 2:3

### Answer:

b) 2:1

### Explanation:

```
Cost price of 1 kg of mixture = $18/120 × 100 = $15.
Using the rule of alligation, the required ratio = (20 - 15):(15 - 15) = 5:0 = 2:1.
```

## 10. The ages of A and B are in the ratio 4:3. After 6 years, the ratio of their ages will be 5:4. Find the present age of A.

a) 16 years

b) 20 years

c) 24 years

d) 28 years

### Answer:

c) 24 years

### Explanation:

```
Let the present ages of A and B be 4x and 3x years respectively.
(4x + 6):(3x + 6) = 5:4. Solving gives x = 6. Present age of A = 4x = 24 years.
```

## 11. The ratio of milk and water in a mixture is 2:3. If 15 litres of water is added, the ratio becomes 2:5. Find the initial quantity of milk in the mixture.

a) 10 litres

b) 12 litres

c) 15 litres

d) 18 litres

### Answer:

a) 10 litres

### Explanation:

```
Let the initial quantities of milk and water be 2x and 3x litres respectively.
2x:(3x + 15) = 2:5. Solving gives x = 5. Initial quantity of milk = 2x = 10 litres.
```

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

a) 8:15

b) 6:11

c) 10:21

d) 5:8

### Answer:

a) 8:15

### Explanation:

```
A:B = 2:3 and B:C = 4:5. To find A:C, make B same in both ratios.
A:B = 2:3 = 8:12 and B:C = 4:5 = 12:15. Therefore, A:C = 8:15.
```

## 13. A sum of money is to be divided among A, B, and C in the ratio 2:3:5. If C gets $200 more than A, find B's share.

a) $150

b) $200

c) $250

d) $300

### Answer:

c) $250

### Explanation:

```
Difference between A's and C's share = 5 - 2 = 3 parts. 3 parts = $200, 1 part = $200/3.
B's share = 3 × $200/3 = $200.
```

## 14. The ratio of the number of boys to girls in a school is 5:4. If there are 200 students in the school, how many are girls?

a) 80

b) 90

c) 100

d) 110

### Answer:

b) 90

### Explanation:

```
Total ratio = 5 + 4 = 9. Number of girls = (4/9) × 200 = 80.
```

## 15. The speed of a boat in still water is to the speed of the current in the ratio 4:1. If the boat covers 120 km downstream in 6 hours, find the speed of the boat in still water.

a) 15 km/hr

b) 20 km/hr

c) 25 km/hr

d) 30 km/hr

### Answer:

b) 20 km/hr

### Explanation:

```
Downstream speed = 120 km / 6 hr = 20 km/hr.
Let the speed of the boat be 4x and the speed of the current be x.
Then, 4x + x = 20 km/hr, 5x = 20 km/hr, x = 4 km/hr. Speed
```

## 15. The speed of a boat in still water is to the speed of the current in the ratio 4:1. If the boat covers 120 km downstream in 6 hours, find the speed of the boat in still water.

a) 15 km/hr

b) 20 km/hr

c) 25 km/hr

d) 30 km/hr

### Answer:

b) 20 km/hr

### Explanation:

```
Downstream speed = 120 km / 6 hr = 20 km/hr.
Let the speed of the boat be 4x and the speed of the current be x.
Then, 4x + x = 20 km/hr, 5x = 20 km/hr, x = 4 km/hr. Speed of the boat = 4x = 16 km/hr.
```

## 16. If two numbers are in the ratio 3:5 and their difference is 16, find the numbers.

a) 18 and 30

b) 24 and 40

c) 27 and 45

d) 30 and 50

### Answer:

b) 24 and 40

### Explanation:

```
Let the numbers be 3x and 5x. Then, 5x - 3x = 16, 2x = 16, x = 8. The numbers are 24 and 40.
```

## 17. In a mixture, the ratio of acid and water is 1:2. If 3 liters of water is added to the mixture, the ratio becomes 1:3. Find the initial quantity of acid in the mixture.

a) 2 liters

b) 3 liters

c) 4 liters

d) 5 liters

### Answer:

b) 3 liters

### Explanation:

```
Let the initial quantities of acid and water be x and 2x liters respectively.
x:(2x + 3) = 1:3. Solving gives x = 3 liters.
```

## 18. A bag contains coins of $1, $2, and $5 in the ratio 4:3:2. If the total amount is $144, how many $5 coins are there?

a) 8

b) 10

c) 12

d) 14

### Answer:

c) 12

### Explanation:

```
Let the number of $1, $2, and $5 coins be 4x, 3x, and 2x respectively.
Total amount = 4x(1) + 3x(2) + 2x(5) = $144.
Solving for x gives x = 6. Number of $5 coins = 2x = 12.
```

## 19. The ages of A, B, and C are in the ratio 3:2:4. If the sum of their ages is 54 years, find A's age.

a) 18 years

b) 20 years

c) 22 years

d) 24 years

### Answer:

a) 18 years

### Explanation:

```
Total ratio = 3 + 2 + 4 = 9. A's age = (3/9) × 54 years = 18 years.
```

## 20. In a 60 litre mixture of milk and water, the ratio of milk to water is 2:1. How much water must be added to make the ratio 1:2?

a) 40 litres

b) 60 litres

c) 80 litres

d) 100 litres

### Answer:

b) 60 litres

### Explanation:

```
Quantity of milk = (2/3) × 60 = 40 litres. To make the ratio of milk to water 1:2, the quantity of water should be 2 × 40 = 80 litres. Water to be added = 80 - 20 = 60 litres.
```