# Ratio and Proportion Aptitude Questions and Answers:

#### Overview:

 Questions and Answers Type: MCQ (Multiple Choice Questions). Main Topic: Quantitative Aptitude. Quantitative Aptitude Sub-topic: Ratio and Proportion Aptitude Questions and Answers. Number of Questions: 10 Questions with Solutions.

1. If $$x : y = 3 : 2$$ then find the value of $$x^2 - y^2 : x^2 + y^2$$?

1. $$13 : 5$$
2. $$5 : 13$$
3. $$7 : 12$$
4. $$12 : 7$$

Answer: (b) $$5 : 13$$

Solution: Given, $$\frac{x}{y} = \frac{3}{2}$$ then $$\frac{x^2}{y^2} = \frac{3^2}{2^2} = \frac{9}{4}$$ Hence, $$\frac{x^2 - y^2}{x^2 + y^2} = \frac{9 - 4}{9 + 4}$$ $$= \frac{5}{13}$$

1. The ratio between two numbers is $$7 : 8$$. If each number is reduced by $$15$$, then the ratio becomes $$4 : 5$$. Find the numbers?

1. $$28 \ and \ 32$$
2. $$32 \ and \ 28$$
3. $$24 \ and \ 30$$
4. $$30 \ and \ 24$$

Answer: (a) $$28 \ and \ 32$$

Solution: Let ratio of two numbers = $$7k : 8k$$

by reducing 12 from each number, $$\frac{7k - 12}{8k - 12} = \frac{4}{5}$$ $$k = 4$$ Hence the numbers = $$28 : 32$$

1. A mixture of wine and water in the ratio of $$5 : 4$$. If two litres of water is added to the mixture the ratio becomes $$7 : 8$$. Find the quantity of wine and water in the mixture?

1. $$6.2 \ and \ 5.4 \ litres$$
2. $$5.4 \ and \ 6.2 \ litres$$
3. $$5.8 \ and \ 4.6 \ litres$$
4. $$4.6 \ and \ 5.8 \ litres$$

Answer: (c) $$5.8 \ and \ 4.6 \ litres$$

Solution: Let the ratio of wine and water in the mixture = $$5k : 4k$$

on adding two litres of water, $$\frac{5k}{4k + 2} = \frac{7}{8}$$ $$k = 1.16$$ Hence, quantity of wine and water $$= 5k : 4k$$ $$= 5.8 : 4.6$$

1. If $$x : y = 5 : 4$$ then find the value of $$x - y : x + y$$?

1. $$1 : 5$$
2. $$5 : 1$$
3. $$9 : 1$$
4. $$1 : 9$$

Answer: (d) $$1 : 9$$

Solution: Given, $$\frac{x}{y} = \frac{5}{4}$$ then, $$\frac{x - y}{x + y} = \frac{5 - 4}{5 + 4}$$ $$= \frac{1}{9}$$

1. A $$500 \ ml$$ mixtute of tea and water in the ratio of $$5 : 3$$. Find how much more water to be included to get a new mixture of tea and water in the ratio of $$5 : 4$$?

1. $$60.2 \ ml$$
2. $$62.5 \ ml$$
3. $$65.3 \ ml$$
4. $$68.5 \ ml$$

Answer: (b) $$62.5 \ ml$$

Solution: quantity of tea in the mixture $$\frac{500}{8} \times 5$$ $$= 312.5 \ ml$$ quantity of water in the mixture $$\frac{500}{8} \times 3$$ $$= 187.5 \ ml$$ Let $$k \ ml$$ water to be added then $$\frac{312.5}{187.5 + k} = \frac{5}{4}$$ $$k = 62.5 \ ml$$

1. Number of students in math and biology in an institute are in the ratio of $$3 : 5$$ respectively. If $$100$$ more students join math and $$50$$ more students join biology, then the ratio becomes $$2 : 3$$. Find the total students in both subjects?

1. $$100$$
2. $$125$$
3. $$175$$
4. $$200$$

Answer: (d) $$200$$

Solution: Let students in math and biology = $$3k : 5k$$

on adding $$100$$ students in math and $$50$$ students in biology, $$\frac{3k + 100}{5k + 50} = \frac{2}{3}$$ $$k = 200$$

1. The ratio of length and breadth of a rectangle is $$2 : 3$$ and by raising length and breadth the ratio becomes $$3 : 4$$. Find the ratio of previous area and present area of rectangle?

1. $$1 : 2$$
2. $$2 : 1$$
3. $$3 : 2$$
4. $$2 : 3$$

Answer: (a) $$1 : 2$$

Solution: let ratio of previous length and breadth of the rectangle = $$2A : 3A$$

then previous area of rectangle = $$2A \times 3A$$ = $$6A^2$$

now let the ratio of present length and breadth of the rectangle = $$3A : 4A$$

then present area of the rectangle = $$3A \times 4A$$ = $$12A^2$$

Hence, the ratio of previous area and present area of rectangle, $$= 6A^2 : 12A^2$$ $$= 1 : 2$$

1. $$250$$ bananas are divided among five boys, $$10$$ girls and $$15$$ women. If the ratio of one boy, one girl and one women is $$5 : 7 : 9$$, then find the share of one girl?

1. $$6.7$$
2. $$7.6$$
3. $$8.2$$
4. $$9.6$$

Answer: (b) $$7.6$$

Solution: Given, the ratio of one boy, one girl and one women = $$5 : 7 : 9$$

then overall ratio of $$5$$ boys, $$10$$ girls and $$15$$ women $$= 5 \times 5 : 7 \times 10 : 9 \times 15$$ $$= 25 : 70 : 135$$ now the share of $$10$$ girls, $$= \frac{250}{230} \times 70$$ $$= 76 \ bananas$$ Hence, the share of one girl $$= \frac{76}{10}$$ $$= 7.6 \ bananas$$

1. The ratio between two numbers is $$5 : 6$$. If each number is reduced by $$25$$, then the ratio becomes $$7 : 8$$. Find the numbers?

1. $$62.5 \ and \ 75$$
2. $$75 \ and \ 62.5$$
3. $$68.5 \ and \ 72$$
4. $$72 \ and \ 68.5$$

Answer: (a) $$62.5 \ and \ 75$$

Solution: Let ratio of two numbers = $$5k : 6k$$

each number is increased by $$25$$, then $$\frac{5k + 25}{6k + 25} = \frac{7}{8}$$ $$k = 12.5$$ Hence the numbers = $$62.5 : 75$$

1. A mixture of milk and water in the ratio of $$4 : 3$$. If $$5$$ litres of water is added to the mixture the ratio becomes $$5 : 4$$. Find the quantity of water in the mixture?

1. $$50 \ litres$$
2. $$75 \ litres$$
3. $$80 \ litres$$
4. $$85 \ litres$$

Answer: (b) $$75 \ litres$$

Solution: Let the ratio of milk and water in the mixture = $$4k : 3k$$

on adding $$5$$ litres of water, $$\frac{4k}{3k + 5} = \frac{5}{4}$$ $$k = 25$$ Hence, quantity of water $$= 3k = 75 \ litres$$