# Ratio and Proportion – Aptitude Questions and Answers

Ratio and proportion are two fundamental concepts for anyone preparing for competitive exams. Whether you’re taking an entrance exam, a government job test, or a qualifying exam for professional certification, you’re likely to encounter questions that require you to use ratio and proportion to solve problems. In this article, we’ll provide you with a comprehensive guide to understanding ratio and proportion in quantitative aptitude, with examples and practice questions to help you master the topic.

To avoid difficulty in solving ratio and proportion problems in SSC and bank exams, practicing problems with solutions and learning the ratio and proportion formulas is essential.

** Practice Quiz **:

## Formulas and Quick Tricks for Ratio and Proportion

- Ratio of two quantities ‘a’ and ‘b’ having the same units is simply a / b and is usually written as a:b
- The equivalence of two ratios is called proportion. If a: b = c : d, then a, b, c, d are said to be in proportion. Here, a x d = b x c
- Mean proportional is the geometric mean. For example, the mean proportion of ‘a’ and ‘b’ is the square root of (a x b)
- If we have two ratios, say a: b and c : d, then (a x c) : (b x d) is called the compounded ratio
- If a: b = c : d, i.e., a/b = c/d, then (a + b) / (a – b) = (c + d) / (c – d) This is called Componendo and Dividendo
- If we say that ‘a’ is directly proportional to ‘b’, it means that a = k x b, where ‘k’ is the constant of proportionality
- If we say that ‘a’ is inversely proportional to ‘b’, it means that a = k / b or a x b = k, where ‘k’ is the constant of proportionality
- If a ratio is multiplied or divided by a certain number, the properties of the ratio do not change. For example, if we multiply 1: 2 by 5, we get 5: 10, which is the same as 1: 2

### Also, check:

## Solved Questions on Ratios and Proportion

### Q 1. If a: b = 5: 9 and b: c = 7: 4, then find a: b: c.

** Solution**:

Here, we make the common term ‘b’ equal in both ratios.

Therefore, we multiply the first ratio by 7 and the second ratio by 9.

So, we have a : b = 35 : 63 and b : c = 63 : 36

Thus, a : b : c = 35 : 63 : 36

### Q 2. Find the mean proportional between 0.23 and 0.24 .

** Solution**:

We know that the mean proportional between ‘a’ and ‘b’ is the square root of (a x b).

=> Required mean proportional = \sqrt(0.23 \times 0.24) = 0.234946802

### Q 3. Divide Rs. 981 in the ratio 5: 4

** Solution**:

The given ratio is 5: 4

Sum of numbers in the ratio = 5 + 4 = 9

We divide Rs. 981 into 9 parts.

981 / 9 = 109

Therefore, Rs. 981 in the ratio 5: 4 = Rs. 981 in the ratio (5 / 9) : (4 / 9)

=> Rs. 981 in the ratio 5 : 4 = (5 x 109) : (4 x 109) = 545 : 436

### Q 4. A bag contains 50 p, 25 p, and 10 p coins in the ratio 2: 5 : 3, amounting to Rs. 510. Find the number of coins of each type.

** Solution**:

Let the common ratio be 100k.

Number of 50 p coins = 200 k

Number of 25 p coins = 500 k

Number of 10 p coins = 300 k

Value of 50 p coins = 0.5 x 200 k = 100 k

Value of 25 p coins = 0.25 x 500 k = 125 k

Value of 10 p coins = 0.1 x 300 k = 30 k

=> Total value of all coins = 100 k + 125 k + 30 k = 255 k = 510 (given)

=> k = 2

Therefore, Number of 50 p coins = 200 k = 400

Number of 25 p coins = 500 k = 1000

Number of 10 p coins = 300 k = 600

### Q 5. A mixture contains sugar solution and colored water in the ratio of 4 : 3. If 10 liters of colored water is added to the mixture, the ratio becomes 4: 5. Find the initial quantity of sugar solution in the given mixture.

** Solution**:

The initial ratio is 4 : 3.

Let ‘k’ be the common ratio.

=> Initial quantity of sugar solution = 4 k

=> Initial quantity of colored water = 3 k

=> Final quantity of sugar solution = 4 k

=> Final quantity of colored water = 3 k + 10

Final ratio = 4 k : 3 k + 10 = 4 : 5

=> k = 5

Therefore, the initial quantity of sugar solution in the given mixture = 4 k = 20 liters

### Q 6. Two friends A and B started a business with an initial capital contribution of Rs. 1 lac and Rs. 2 lacs. At the end of the year, the business made a profit of Rs. 30,000. Find the share of each in the profit.

** Solution**:

We know that if the time period of investment is the same, profit/loss is divided by the ratio of the value of the investment.

=> Ratio of value of investment of A and B = 1,00,000 : 2,00,000 = 1 : 2

=> Ratio of share in profit = 1 : 2

=> Share of A in profit = (1/3) x 30,000 = Rs. 10,000

=> Share of B in profit = (2/3) x 30,000 = Rs. 20,000

### Q 7. Three friends A, B, and C started a business, each investing Rs. 10,000. After 5 months A withdrew Rs. 3000, B withdrew Rs. 2000 and C invested Rs. 3000 more. At the end of the year, a total profit of Rs. 34,600 was recorded. Find the share of each.

** Solution**:

We know that if the period of investment is not uniform, the gains/losses from the business are divided in the ratio of their inputs, where input is calculated as the product of an amount of investment and the time period of investment.

So, input = value of investment x period of investment, and here, the period of investment would be broken into parts as the investment is not uniform throughout the time period.

A’s input = (10,000 x 5) + (7,000 x 7) = 99,000

B’s input = (10,000 x 5) + (8,000 x 7) = 1,06,000

C’s input = (10,000 x 5) + (13,000 x 7) = 1,41,000

=> A : B : C = 99000 : 106000 : 141000

=> A : B : C = 99 : 106 : 141

=> A : B : C = (99 / 346) : (106 / 346) : (141 / 346)

Thus, A’s share = (99 / 346) x 34600 = Rs. 9900

B’s share = (106 / 346) x 34600 = Rs. 10600

C’s share = (141 / 346) x 34600 = Rs. 14100

### Q 8. A invested Rs. 70,000 in a business. After a few months, B joined him with Rs. 60,000. At the end of the year, the total profit was divided between them in the ratio of 2: 1. After how many months did B join?

** Solution**:

Let A work alone for ‘n’ months.

=> A’s input = 70,000 x 12

=> B’s input = 60,000 x (12 – n)

So, (70,000 x 12) / [60,000 x (12 – n)] = 2 / 1

=> (7 x 12) / [6 x (12 – n)] = 2 / 1

=> 12 – n = 7

=> n = 5

Therefore, B joined after 5 months.

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Test your knowledge of ratio and proportion in Quantitative Aptitude with the quiz linked below, containing numerous practice questions to help you master the topic:-

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