Practice MCQ Questions and Answer on Ratio

71.

A person spends Rs. 8100 in buying some tables at Rs. 1200 each and some chairs at Rs. 300 each. The ratio of the number of chairs to that of tables when the maximum possible number of tables is purchased,

(A) 1 : 2
(B) 1 : 4
(C) 2 : 1
(D) 5 : 7

Solution: Maximum possible number of tables = 6 [∵ 1200 × 6 = 7200] Number of chairs purchased $\begin{aligned} = \frac{8100 - 7200}{300} = \frac{900}{300} = 3 \\ Hence, \\ Required ratio = 3 : 6 \\ = 1 : 2 \end{aligned}$

72.

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

73.

Two bottles contain acid and water in the ratio 2 : 3 and 1 : 2 respectively. These are mixed in the ratio 1 : 3. What is the ratio of acid and water in the new mixture = ?

(A) 7 : 13
(B) 11 : 57
(C) 23 : 37
(D) 1 : 3

Solution: Let 1 bottle of acid is 30litre and consider the first bottle as A and second bottle as B. Ratio of Acid and water in bottle A = 2 : 3 Volume of Acid in bottle A = $\frac{2}{5} \times 30 = 12$ Volume of Water in bottle A = $\frac{3}{5} \times 30 = 18$ Ratio of Acid and water in bottle A = 1 : 2 Volume of Acid in bottle A = $\frac{1}{3} \times 30 = 10$ Volume of Water in bottle A = $\frac{2}{3} \times 30 = 20$ Now 1 bottle of A and 3 bottles of B mixed together Volume of Acid in new mixture = 12 + 3 × 10 = 42 Volume of water in new mixture = 18 + 3 × 20 = 78 Ratio of Acid and water in new mixture = 42 : 78 = 7 : 13

74.

In two alloys A and B the ratio of Zinc and Tin is 5 : 2 and 3 : 4 respectively. 7 kg of the alloy A and 21 kg of the alloy B are mixed together to form a new alloy. What will be the ratio of Zinc and Tin tin the new alloy ?

(A) 2 : 1
(B) 1 : 2
(C) 2 : 3
(D) 1 : 1

Solution: Zinc : Tin A 5x : 2x = 7x B 3y : 4y = 7y ⇒ A ⇒ 7x = 7 kg x = 1 kg ∴ Zinc in alloy A ⇒ 5kg Tin in alloy A ⇒ 2 kg ⇒ B ⇒ 7y = 21 kg y = 3 kg Zinc in alloy B ⇒ 3 × 3 = 9 kg Tin in alloy B ⇒ 3 × 4 = 12 kg ∴ After mix - up the ratio of Zinc and Tin in new alloy $\begin{aligned} Zinc : Tin \\ A 5 : 2 \\ B 9 : 12 \\ \overset{―}{A + B : 14 14} \\ 1 : 1 \end{aligned}$

75.

The ratio of the income of A and B in the last year was 4 : 3. The ratios of their individual incomes in the last year and the present year are 3 : 4 and 5 : 6, respectively. If their total income in the present year in Rs. 24.12 lakhs, then the sum of the income (in Rs. lakh) of A in the last year and that of B in the present year is:

(A) 22.17
(B) 10.98
(C) 20.52
(D) 21.28

Solution: $\begin{matrix} Last year & Current year \\ A \to & 3_{\times 5 \times 4} = 60 & 4_{\times 5 \times 4} = 80 \\ B \to & 5_{\times 3 \times 3} = 45 & 6_{\times 3 \times 3} = 54 \end{matrix}$ The ratio of income of A and B in the last year is 4 : 3. So we're making last year's income 60, 45. Present age ratio of both = 80 : 54 Sum of present age of both = 80 + 54 = 134 units 134 units → 24.12 lakh 1 unit → $\frac{24.12}{134}$ Sum of income of A in final year and income of B in present year = 60 + 54 = 114 114 units → $\frac{24.12}{134}$ × 114 = 20.52 Sum of income of A in final year and income of B in present year = 20.52 lakh Alternate solution $\begin{matrix} A & B \\ Previous year \to & 4 x & 3 x \end{matrix}$ A's present salary : Ratio of final year to present year = 3 : 4 3 units = 4x 4 units $= 4 x \times \frac{4}{3} = \frac{16}{3} x$ B's present salary : Final year and present year = 5 : 6 5 units = 3x 6 units $= 3 x \times \frac{6}{5} = \frac{18}{5} x$ $\begin{matrix} A & B \\ Present year \to & \frac{16}{3} x & \frac{18}{5} x \end{matrix}$ $\begin{aligned} \frac{16}{3} x + \frac{18}{5} x = \frac{134}{15} x \to 24.12 lakh \\ x = \frac{24.12 \times 15}{134} \end{aligned}$ Final year income of A and Present year income of B. $\begin{aligned} = 4 x + \frac{18}{5} x = \frac{38}{5} x \\ \frac{38}{5} x \to \frac{24.12 \times 15}{134} \times \frac{38}{5} = 20.52 \end{aligned}$ Final year income of A and Present year income of B = 20.52 lakh

76.

If $a : b : c = \frac{1}{4} : \frac{1}{3} : \frac{1}{2},$ ÃÂÃÂ ÃÂÃÂ then $\frac{a}{b} : \frac{b}{c} : \frac{c}{a} = ?$

(A) 12 : 9 : 8
(B) 9 : 8 : 24
(C) 8 : 9 : 24
(D) 9 : 12 : 8

Solution: $\begin{aligned} a : b : c = \frac{1}{4} : \frac{1}{3} : \frac{1}{2} \\ a : b : c = 3 : 4 : 6 \\ \frac{a}{b} : \frac{b}{c} : \frac{c}{a} = \frac{3}{4} : \frac{4}{6} : \frac{6}{3} = 9 : 8 : 24 \end{aligned}$

77.

Which of the following represents ab = 64?

(A) 8 : a = 8 : b
(B) a : 16 = 6 : 4
(C) a : 8 = b : 8
(D) 32 : a = b : 2

78.

If A : B = 7 : 9 and B : C = 3 : 5 then A : B : C is equal to = ?

(A) 7 : 9 : 5
(B) 21 : 35 : 45
(C) 7 : 9 : 15
(D) 7 : 3 : 15

79.

The ratio of ducks and frogs in a pond is 37 : 39 respectively. The average number of ducks and frogs in the pond is 152. What is the number of frogs in the pond ?

(A) 148
(B) 152
(C) 156
(D) 144

Solution: Ratio of Ducks and Frogs in Pond = 37 : 39 Average of Ducks and Frogs in Pond = 152 So, total number of Ducks and Frogs in the Pond = 2 × 152 = 304 ∴ Number of Frogs = $\frac{304 \times 39}{76}$ = 156

80.

The ratio of milk to water in three containers of equal capacity is 3 : 2, 7 : 3 and 11 : 4 respectively. The contents of the three containers are mixed together. What is the ratio of milk to water after mixing ?

(A) 19 : 4
(B) 7 : 3
(C) 61 : 29
(D) 41 : 18

Solution: $\begin{aligned} Milk in the mixture \\ = (\frac{3}{5} + \frac{7}{10} + \frac{11}{15}) units \\ = \frac{61}{30} units . \\ Water in the mixture \\ = (\frac{2}{5} + \frac{3}{10} + \frac{4}{15}) units \\ = \frac{29}{30} units . \\ ∴ Required ratio \\ = \frac{61}{30} : \frac{29}{30} \\ = 61 : 29 \end{aligned}$

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Practice MCQ Questions and Answer on Ratio

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