Practice MCQ Questions and Answer on Ratio

31.

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 $\begin{aligned} ∴ \frac{3 \times x + 5 \times 7 + 7 \times x}{3 \times 2 x + 5 \times 2 x + 7 \times 2 x} \times 1 \\ \Rightarrow \frac{15 x}{30 x} \\ \Rightarrow \frac{1}{2} \end{aligned}$

32.

A dishonest milk man mixed 1 liter of water for every 3 liters of milk and thus made up 36 liters of milk. If he now adds 15 liters of milk to mixture, find the ratio of milk and water in the new mixture:

(A) 12 : 5
(B) 14 : 3
(C) 7 : 2
(D) 9 : 4

33.

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

(A) 11
(B) 19
(C) 23
(D) 7

Solution: $\frac{3 x + 5}{5 x - 2} = \frac{2}{3}$ ⇒ Cross multiply the equation $\begin{aligned} 9 x + 15 = 10 x - 4 \\ x = 19 \end{aligned}$

34.

If x : y = 3 : 4, then the value of (4x - y) : (2x + 3y) is = ?

(A) 4 : 9
(B) 8 : 9
(C) 4 : 3
(D) 8 : 3

Solution: $\begin{aligned} x : y = 3 : 4 \\ ∴ \frac{x}{y} = \frac{3}{4} \\ \Rightarrow \frac{4 x - y}{2 x + 3 y} \\ \Rightarrow \frac{y (4 \frac{x}{y} - 1)}{y (2 \frac{x}{y} + 3)} \\ \Rightarrow \frac{4 \times \frac{3}{4} - 1}{2 \times \frac{3}{4} + 3} \\ \Rightarrow \frac{(3 - 1) \times 2}{3 + 6} \\ \Rightarrow \frac{4}{9} \\ \Rightarrow 4 : 9 \end{aligned}$

35.

If $A$ : $B$ = $\frac{1}{2}$ : $\frac{3}{8},$ ÃÂÃÂ $B$ : $C$ = $\frac{1}{3}$ : $\frac{5}{9}$ and $C$ : $D$ = $\frac{5}{6}$ : $\frac{3}{4},$ ÃÂÃÂ Then the ratio of A : B : C : D is ?

(A) 6 : 4 : 8 : 10
(B) 6 : 8 : 9 : 10
(C) 8 : 6 : 10 : 9
(D) 4 : 6 : 8 : 10

Solution: $\begin{aligned} A : B = \frac{1}{2} : \frac{3}{8}, \\ \frac{A}{B} = \frac{4}{3} \\ B : C = \frac{1}{3} : \frac{5}{9}, \\ \frac{B}{C} = \frac{1}{3} \times \frac{9}{5} = \frac{3}{5} \\ C : D = \frac{5}{6} : \frac{3}{4}, \\ \frac{C}{D} = \frac{5 \times 4}{6 \times 3} = \frac{10}{9} \\ A : B : C : D \\ 4 : 3 \\ 3 : 5 \\ 10 : 9 \\ \Rightarrow A : B : C : D \\ 8 : 6 : 10 : 9 \end{aligned}$

36.

Three numbers are in the ratio 5 : 7 : 12. If the sum of the first and the third is greater than the second by 50. The sum of the three numbers is = ?

(A) 125
(B) 120
(C) 95
(D) 85

37.

A box contains 280 coins of one rupee, 50 paise and 25 paise. The value of each kind of the coins are in the ratio of 8 : 4 : 3. Then the number of 50 paise coins is = ?

(A) 70
(B) 60
(C) 80
(D) 90

Solution: Rs. 1 : 50 P : 25 p Values of coins 8x : 11x : 3x Number of coins 8x×1 : 4x×2 : 3x×4 8x : 8x : 12x $\begin{aligned} ∴ Total coins \\ \Rightarrow 8 x + 8 x + 12 x = 28 x \\ \Rightarrow 28 x = 280 (given) \\ \Rightarrow x = \frac{280}{28} \\ \Rightarrow x = 10 \end{aligned}$ ∴ Number of 50 P coins are 8x = 8 × 10 = 80

38.

If 0.75 : x :: 5 : 8, then x is equal to:

(A) 1.12
(B) 1.2
(C) 1.25
(D) 1.30

Solution: $\begin{aligned} x \times 5 = 0.75 \times 8 \\ \Rightarrow x = \frac{6}{5} \\ \Rightarrow x = 1.2 \end{aligned}$

39.

Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

(A) 2 : 5
(B) 3 : 5
(C) 4 : 5
(D) 6 : 7

Solution: $\begin{aligned} Let the third number be x \\ Then, first number \\ = 120 % of x = \frac{120 x}{100} = \frac{6 x}{5} \\ Second number \\ = 150 % of x = \frac{150 x}{100} = \frac{3 x}{2} \\ ∴ Ratio of first two numbers \\ = \frac{6 x}{5} : \frac{3 x}{2} = 12 x : 15 x = 4 : 5 \end{aligned}$

40.

Rita invested 25% more than sunil. Sunil invested 30% less than Abhinav, who invested Rs. 6000. What is the ratio of the amount that Rita invested to the total amount by all of them together ?

(A) 35 : 104
(B) 13 : 29
(C) 101 : 36
(D) 35 : 103

Solution: $\begin{aligned} Abhinav's investment \\ = Rs . 6000 \\ Sunil's investment \\ = (100 - 30) % of Rs . 6000 \\ = 70 % of Rs . 6000 \\ = Rs . (\frac{70}{100} \times 6000) \\ = Rs .4200 \\ Rita's investment \\ = (100 + 25) % of Rs . 4200 \\ = 125 % of Rs . 4200 \\ = Rs . (\frac{125}{100} \times 4200) \\ = Rs . 5250 \\ Total amount invested \\ = Rs . (6000 + 4200 + 5250) \\ = Rs . 15450. \\ ∴ Required Ratio \\ = 5250 : 15450 \\ = 35 : 103 \end{aligned}$

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Practice MCQ Questions and Answer on Ratio

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