Practice MCQ Questions and Answer on Ratio

51.

If $\frac{x}{2} = \frac{y}{3} = \frac{z}{4} =$ ÃÂÃÂ $\frac{2 x - 3 y + 5 z}{k},$ ÃÂÃÂ ÃÂÃÂ then the value of k is -

(A) 12
(B) 15
(C) 16
(D) 18

Solution: $\begin{aligned} Let \frac{x}{2} = \frac{y}{3} = \frac{z}{4} = l \\ Then, \\ = x = 2 l, y = 3 l, z = 4 l \\ ∴ \frac{x}{2} = \frac{2 x - 3 y + 5 z}{k} \\ \Rightarrow \frac{2 l}{2} = \frac{2 \times 2 l - 3 \times 3 l + 5 \times 4 l}{k} \\ \Rightarrow k = 4 - 9 + 20 = 15 \end{aligned}$

52.

In a business, the ratio of the capitals of A and B is 2 : 1, that of B and C is 4 : 3 and that of D and C is 6 : 5. Then the ratio of the capitals of A and D is -

(A) 9 : 20
(B) 3 : 5
(C) 5 : 3
(D) 20 : 9

Solution: $\begin{aligned} = \frac{A}{B} = \frac{2}{1}, \frac{B}{C} = \frac{4}{3}, \frac{C}{D} = \frac{5}{6} \\ \Rightarrow \frac{A}{D} = (\frac{A}{B} \times \frac{B}{C} \times \frac{C}{D}) \\ = (\frac{2}{1} \times \frac{4}{3} \times \frac{5}{6}) \\ = \frac{20}{9} \\ \Rightarrow A : D = 20 : 9 \end{aligned}$

53.

If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?

(A) 2 : 5
(B) 3 : 7
(C) 5 : 3
(D) 7 : 3

Solution: $\begin{aligned} Let 40 % of A = \frac{2}{3} B \\ Then, \frac{40 A}{100} = \frac{2 B}{3} \\ \Rightarrow \frac{2 A}{5} = \frac{2 B}{3} \\ \Rightarrow \frac{A}{B} = \frac{2}{3} \times \frac{5}{2} = \frac{5}{3} \\ ∴ A : B = 5 : 3 \end{aligned}$

54.

If a : b = c : d = e : f = 1 : 2, then (3a + 5c + 7e) : (3b + 5d + 7f) is = ?

(A) 8 : 7
(B) 2 : 1
(C) 1 : 4
(D) 1 : 2

Solution: a : b = 1 : 2 c : d = 1 : 2 e : f = 1 : 2 ∴ a = x, b = 2x, c = x, d = 2x, e = x, f = 2x $\begin{aligned} ∴ \frac{3 \times x + 5 \times 7 + 7 \times x}{3 \times 2 x + 5 \times 2 x + 7 \times 2 x} \times 1 \\ \Rightarrow \frac{15 x}{30 x} \\ \Rightarrow \frac{1}{2} \end{aligned}$

55.

The weight of Mr. Gupta and Mrs. Gupta are in the ratio 7 : 8 and their total weight is 120 kg. After taking a dieting course Mr. Gupta reduces by 6 kg and the ratio between their weights change to 5 : 6, so Mrs. Gupta has reduced by = ?

(A) 2 kg
(B) 4 kg
(C) 3 kg
(D) 5 kg

Solution: Mr. : Mrs. Before 7x : 8x After 5y : 6y Before 7x + 8x = 120 ⇒ 15x = 120 ⇒ x = 8 ∴ Mr. Gupta = 7 × 8 = 56 Mrs. Gupta = 8 × 8 = 64 ∴ After losing 6kg by Mr. Gupta the ratio becomes 5 : 6 ⇒ Let Mrs. Gupta loss x kg $\begin{aligned} ∴ \frac{56 - 6}{64 - x} \times \frac{5}{6} \\ (Cross multiplication) \end{aligned}$ ⇒ 300 = 320 - 5x ⇒ 5x = 20 ∴ x = 4 kg

56.

The sum of three numbers is 280. If the ratio between the first and second numbers is 2 : 3 and the ratio between second and third numbers is 4 : 5, then find the second number.

(A) 80
(B) 90
(C) 86
(D) 96

Solution: $\begin{aligned} I^{st} I I^{nd} II I^{rd} \\ 2 : 3 \\ 4 : 5 \\ \overset{―}{8 : 12 : 15} \\ 35 unit \to 280 \\ 1 unit \to 8 \\ 12 unit \to 12 \times 8 = 96 \end{aligned}$

57.

The fourth proportional to 0.12, 0.21 and 8 is-

(A) 8.9
(B) 14
(C) 17
(D) 56

Solution: Let the fourth proportional to 0.12, 0.21 and 8 be x $\begin{aligned} Then, \\ = 0 .12 : 0 .21 :: 8 : x \\ \Rightarrow 0 .12 x = 0.21 \times 8 \\ \Rightarrow x = \frac{0.21 \times 8}{0.12} \\ = \frac{21 \times 8}{12} \\ = 14. \end{aligned}$

58.

A sum of Rs. 1250 has to distributed among A, B, C and D. Total share of B and D is equal to (14/11) of total share of A and C. Share of D is half of share of A. Share of C is 1.2 of share of A. What are the shares of A, B, C and D respectively?

(A) Rs. 250, Rs. 575, Rs. 300, Rs. 175
(B) Rs. 250, Rs. 575, Rs.300, Rs. 125
(C) Rs. 350, Rs. 525, Rs. 300, Rs. 125
(D) Rs. 250, Rs. 525, Rs. 300, Rs. 125

Solution: $\begin{aligned} A + B + C + D = 1250. . . . . . . (1) \\ \frac{B + D}{A + C} = \frac{14}{11} . . . . . . . (2) \\ \frac{D}{A} = \frac{1}{2} \\ \frac{C}{A} = \frac{1.2}{1} = \frac{6}{5} \\ From equation (1) \\ 14 + 11 = 1250 \\ 25 units = 1250 \\ 1 unit = 50 \\ C's share 6 units \to 300 \\ A's share 5 units \to 250 \end{aligned}$ $\Rightarrow \frac{D}{A} = \frac{1}{2} \begin{matrix} \to 125 \\ \to 250 \end{matrix}$ $\begin{aligned} From equation (1) \\ A + B + C + D = 1250 \\ 250 + B + 300 + 125 = 1250 \\ B = 575 \end{aligned}$

59.

The sum of three numbers is 116. The second number and the third number are in the ratio of 9 : 16 while the first number and the third number are in the ratio of 1 : 4. Find the second number.

(A) 8
(B) 16
(C) 64
(D) Cannot be determined

Solution: Answer & Solution Answer: Option E Solution: $\begin{aligned} Second : Third \\ = 9 : 16 \\ Third : first \\ = 4 : 1 \\ = 16 : 4 \\ ∴ Second : Third : first \\ = 9 : 16 : 4 \\ Second number \\ = (116 \times \frac{9}{29}) \\ = 36 \end{aligned}$

60.

Rs. 3,600 is divided between Seema, Komal and Rita, such that the ratios of the shares of Seema : Komal = 1.5 : 2 and Komal : Rita = 2 : 2.5. Find Rita's share.

(A) Rs. 1,500
(B) Rs. 1,300
(C) Rs. 1,400
(D) Rs. 1,200

Solution: Ratio of shares of Seema and Komal = 1.5x : 2x Ratio of shares of Komal and Rita = 2x : 2.5x Ratio of shares of Seema, Komal and Rita = 1.5x : 2x : 2.5x According to the question 1.5x + 2x + 2.5x = 3600 ⇒ 6x = 3600 ⇒ x = $\frac{3600}{6}$ ⇒ x = 600 ∴ Share of Rita = 2.5 × 600 = Rs. 1,500

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Practice MCQ Questions and Answer on Ratio

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