Practice MCQ Questions and Answer on Ratio

121.

If two number are in the ratio 2 : 3 and the ratio becomes 3 : 4 when 8 is added to both the numbers, then the sum of the two numbers is = ?

(A) 90
(B) 50
(C) 60
(D) 40

Solution: Let the 2 number be (2x, 3x) According to the question, $\begin{aligned} \Rightarrow \frac{2 x + 8}{3 x + 8} = \frac{3}{4} \\ \Rightarrow 8 x + 32 = 9 x + 24 \\ \Rightarrow x = 8 \end{aligned}$ Therefore, the sum of the two numbers is = 2x + 3x = 5x = 5 × 8 = 40

122.

The present ratio of ages of A and B is 4 : 5. 18 years ago, this ratio was 11 : 16. Find the sum total of their present ages.

(A) 90 years
(B) 105 years
(C) 110 years
(D) 80 years

Solution: Let present age of A and B be 4x and 5x 18 years ago their ages $\frac{4 x - 18}{5 x - 18} = \frac{11}{16}$ Or, 64x - 288 = 55x - 198 Or, 64x - 55x = -198 + 288 Or, 9x = 90 Or, x = $\frac{90}{9}$ = 10 Sum of the present ages = 40 + 50 = 90 years

123.

If x² + 4y² = 4xy, then x : y is -

(A) 1 : 1
(B) 1 : 2
(C) 2 : 1
(D) 1 : 4

Solution: $\begin{aligned} = x^{2} + 4 y^{2} = 4 x y \\ \Rightarrow x^{2} - 4 x y + 4 y^{2} = 0 \\ \Rightarrow (x - 2 y^{2}) = 0 \\ \Rightarrow x = 2 y \\ \Rightarrow \frac{x}{y} = 2 \\ \Rightarrow x : y = 2 : 1 \end{aligned}$

124.

Two numbers are in the ratio 3 : 5. If 6 is added to both of them, the ratio becomes 2 : 3. The numbers are = ?

(A) 21 and 35
(B) 30 and 50
(C) 24 and 40
(D) 18 and 30

Solution: Let numbers are = 3x and 5x ∴ According to question, $\begin{aligned} \Rightarrow \frac{3 x + 6}{5 x + 6} = \frac{2}{3} \\ \Rightarrow 9 x + 18 = 10 x + 12 \\ \Rightarrow x = 6 \\ So, numbers are \\ 3 x = 3 \times 6 = 18 \\ 5 x = 5 \times 6 = 30 \end{aligned}$

125.

The salaries of A, B and C are in the ratio 1 : 3 : 4. If the salaries are increased 5%, 10% and 15% respectively. Then the increased salaries will be in the ratio = ?

(A) 20 : 66 : 95
(B) 21 : 66 : 95
(C) 21 : 66 : 92
(D) 19 : 66 : 92

126.

The monthly incomes of A and B are in ratio 3 : 5 and the ratio of their saving is 2 : 3. If the income of B is equal to three times the saving of A, then what is the ratio of the expenditures of A and B?

(A) 5 : 8
(B) 8 : 15
(C) 3 : 7
(D) 7 : 11

Solution: $\begin{matrix} A & B \\ Income \to & 3 x & : & 5 x \\ Saving \to & 2 y & : & 3 y \end{matrix}$ $\begin{aligned} 5 x = 3 \times 2 y \\ \frac{x}{y} = \frac{6}{5} \end{aligned}$ $\begin{matrix} A B \\ Income \to & 18 30 \\ Saving \to & 10 15 \\ Expenditure \to & \overset{―}{8 : 15} \end{matrix}$

127.

A vessel of capacity 2 litre has 25% alcohol and another vessel of capacity 6 litre had 40% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. what is the new concentration of mixture ?

(A) 29%
(B) 49%
(C) 31%
(D) 71%

Solution: Amount of alcohol in first vessel, = 25% of 2 litre = 0.25 × 2 = 0.5 litre Amount of alcohol in second vessel, = 40% of 6 litre = 0.4 × 6 = 2.4 litre Total amount of alcohol out of 10 litres of mixture is 0.5 + 2.4 = 2.9 litre Thus, Concentration of the mixture is, $\frac{2.9 \times 100}{10}$ = 29%

128.

Rs. 33630 are divided among A, B and C in such a manner that the ratio of the amount of A to that of B is 3 : 7 and the ratio of the amount of B to that of C is 6 : 5. The amount of money received by B is = ?

(A) Rs. 14868
(B) Rs. 16257
(C) Rs. 13290
(D) Rs. 12390

129.

One year ago the ratio of the ages of Sarika and Gouri was 3 : 4 respectively. One year hence the ratio of their ages will be 10 : 13 respectively. What is Sarika's present age ?

(A) 18 years
(B) 20 years
(C) 26 years
(D) Cannot be determined

Solution: Answer & Solution Answer: Option E Solution: Let Sarika's and Gauri's ages one year ago be 3x and 4x years respectively Sarika's age 1 year hence = (3x + 2) years Gauri's age 1 year hence = (4x + 2) $\begin{aligned} ∴ \frac{3 x + 2}{4 x + 2} = \frac{10}{13} \\ \Rightarrow 13 (3 x + 2) = 10 (4 x + 2) \\ \Rightarrow 39 x + 26 = 40 x + 20 \\ \Rightarrow x = 6 \end{aligned}$ Hence, Sarika's present age = 3x + 1 = (3 × 6 + 1) years = 19 years

130.

200 litres of a mixture contains milk and water in the ratio 17 : 3. After the addition of some more milk to it, the ratio of milk to water in the resulting mixture becomes 7 : 1. The quantity of milk added to it was =?

(A) 20 Litres
(B) 40 Litres
(C) 60 Litres
(D) 80 Litres

Solution: Milk : water = 17 : 3 = 17x : 3x ∴ 17x + 3x = 200 ⇒ x =10 litre Milk = 170 litre and water = 30 litre in initial mixture. Let 'y' litre of milk added in mixture i.e. 170 + y : 30 = 7 : 1 ⇒ $\frac{170 + y}{30} = \frac{7}{1}$ ∴ y = 210 - 170 = 40 litre

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Practice MCQ Questions and Answer on Ratio

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