# 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. In a mixture of $$35$$ litres, the ratio of milk and water is $$5 : 2$$. find how much water must be added to this mixture so that the ratio of milk and water becomes $$3 : 4$$?

1. $$24.2 \ litres$$
2. $$22.2 \ litres$$
3. $$23.3 \ litres$$
4. $$23.8 \ litres$$

Answer: (c) $$23.3 \ litres$$

Solution: Let the ratio of milk and water = $$5k : 2k$$

the given mixture is $$35$$ litres, so $$25 : 10 = 5k : 2k$$ now the amount of water k must be added to the given ratio become $$3 : 4$$, $$25 : (10 + k) = 3 : 4$$ $$\frac{25}{10 + k} = \frac{3}{4}$$ $$10 + k = \frac{100}{3}$$ $$k = 23.3 \ litres$$

1. Find the ratio of squares of the numbers, if three numbers are in the ratio of $$2 : 3 : 5$$ and half the sum of the numbers is $$10$$?

1. $$16 : 36 : 81$$
2. $$16 : 36 : 100$$
3. $$36 : 49 : 81$$
4. $$36 : 81 : 100$$

Answer: (b) $$16 : 36 : 100$$

Solution: Let ratio is $$2k : 3k : 5k$$, then $$\frac{2k + 3k + 5k}{2} = 10$$ $$k = 2$$ then the numbers are, $$4 : 6 : 10$$ and square of numbers are $$16 : 36 : 100$$

1. The ratio of ages of $$x$$ and $$y$$ is $$3 : 2$$ at present and after $$10$$ years, the ratio will become $$5 : 4$$, find the present age of $$x$$?

1. $$10 \ years$$
2. $$12 \ years$$
3. $$15 \ years$$
4. $$20 \ years$$

Answer: (c) $$15 \ years$$

Solution: Let their present ages = $$3k : 2k$$

then after $$10$$ years, $$\frac{3k + 10}{2k + 10} = \frac{5}{4}$$ $$k = 5$$ then the present ages of $$x$$ and $$y$$, $$x : y = 3k : 2k$$ $$x : y = 15 : 10$$ Hence, present age of $$x$$ is $$15$$ years.

1. If $$115$$ books was distributed among three students in the ratio of $$2/3 : 3/4 : 1/2$$, then find how many books the first student got?

1. $$25 \ books$$
2. $$30 \ books$$
3. $$40 \ books$$
4. $$45 \ books$$

Answer: (c) $$40 \ books$$

Solution: The ratio of books given, $$\frac{2}{3} : \frac{3}{4} : \frac{1}{2}$$ $$= \frac{8 : 9 : 6}{12}$$ so the books in the ratio $$8k : 9k : 6k$$ are distributed, then $$8k + 9k + 6k = 115$$ $$k = 5$$ now the ratio $$= 8k : 9k : 6k$$ $$= 40 : 45 : 30$$ Hence, the first student got $$40$$ books.

1. If a mixture contains milk and water in the ratio of $$3 : 1$$ and on adding two litres of water, the ratio becomes $$5 : 3$$, then find the quantity of milk in the mixture?

1. $$10.2 \ litres$$
2. $$12.5 \ litres$$
3. $$15.5 \ litres$$
4. $$16.8 \ litres$$

Answer: (b) $$12.5 \ litres$$

Solution: Let the present ratio of milk and water = $$3k : k$$

then on adding two litres of water, $$3k : (k + 2) = 5 : 3$$ $$\frac{3k}{k + 2} = \frac{5}{3}$$ $$k = 2.5$$ so the ratio after adding two litres of water, $$= 5k : 3k$$ $$= 5 \times 2.5 : 3 \times 2.5$$ $$= 12.5 : 7.5$$ Hence, the quantity of milk = $$12.5 \ litres$$

1. If by adding $$5$$ on the ratio of the numbers $$5 : 7$$, it becomes $$7 : 9$$, then find the lower number?

1. $$20.5$$
2. $$16.5$$
3. $$15.5$$
4. $$12.5$$

Answer: (d) $$12.5$$

Solution: Let the ratio = $$5k : 7k$$

on adding $$5$$ ratio becomes $$7 : 9$$, then $$\frac{5k + 5}{7k + 5} =\frac{7}{9}$$ $$k = 2.5$$ then ratio $$= 5k : 7k$$ $$= 5 \times 2.5 : 7 \times 2.5$$ $$= 12.5 : 17.5$$ Hence, the lower number = $$12.5$$

1. Find the fourth proportional of the numbers $$10$$, $$15$$ and $$20$$?

1. $$20$$
2. $$30$$
3. $$40$$
4. $$50$$

Answer: (b) $$30$$

Solution: Let k is the fourth proportional, then $$= 10 : 15 :: 20 : k$$ $$\frac{10}{15} = \frac{20}{k}$$ $$k = 30$$

1. Find the mean proportional of $$8$$ and $$2$$?

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

Answer: (a) $$4$$

Solution: Let mean proportional = $$k$$, then $$8 : k :: k : 2$$ $$\frac{8}{k} = \frac{k}{2}$$ $$k^2 = 16$$ $$k = \sqrt{16}$$ $$k = 4$$

1. Find the third proportional of $$2$$ and $$4$$?

1. $$4$$
2. $$6$$
3. $$8$$
4. $$10$$

Answer: (c) $$8$$

Solution: Let third proportional = $$k$$, then $$2 : 4 :: 4 : k$$ $$\frac{2}{4} = \frac{4}{k}$$ $$k = 8$$

1. If the ratio of two numbers is $$9 : 6$$ and their sum is $$150$$, then find the greater number?

1. $$50$$
2. $$70$$
3. $$80$$
4. $$90$$

Answer: (d) $$90$$

Solution: Let numbers = $$9k : 6k$$, then $$9k + 6k = 150$$ $$k = 10$$ then numbers are,$$9k : 6k = 90 : 60$$ Hence, the greater number is $$90$$