Practice MCQ Questions and Answer on Ratio

31.

If p : q = 3 : 4, r : s = 8 : 5 and x : y = 10 : 6, then psx : qry is equal to.

(A) $\frac{16}{25}$
(B) $\frac{25}{32}$
(C) $2$
(D) $\frac{75}{32}$

Solution: $\begin{aligned} = \frac{p}{q} = \frac{3}{4}, \frac{r}{s} = \frac{8}{5}, \frac{x}{y} = \frac{10}{6} \\ \Rightarrow p = \frac{3 q}{4}, r = \frac{8 s}{5}, x = \frac{5 y}{3} \\ ∴ \frac{p s x}{q r y} = \frac{\frac{3 q}{4} \times s \times \frac{5 y}{3}}{q \times \frac{8 s}{5} \times y} \\ = \frac{\frac{5}{4} q s y}{\frac{8}{5} q s y} \\ = \frac{5}{4} \times \frac{5}{8} \\ = \frac{25}{32} \end{aligned}$

32.

Tom is chasing Jerry. In the same interval of time Tom jumps 8 times while Jerry jumps 6 times. But the distance covered by Tom in 7 Jumps is equal to the distance covered by Jerry in 5 Jumps. The ratio of speed of Tom and Jerry is:

(A) 48 : 35
(B) 28 : 15
(C) 24 : 20
(D) 20 : 21

Solution: Given; 7 jumps of Tom = 5 jumps of Jerry Or, $\frac{Tom}{Jerry} = \frac{5}{7}$ Let Jerry's 1 leap = 7 meter and Tom's 1 leap = 5 meter Then, ratio of speed of Tom and Jerry = $\frac{8 \times 5}{6 \times 7}$ = $\frac{40}{42}$ = 20 : 21

33.

A bag has coins of 50 paisa, 25 paisa and 10 paisa in the respective ratio of 5 : 8 : 3 whose total value is Rs.144. Find the number of 50 paisa coins.

(A) 163
(B) 175
(C) 200
(D) 150

Solution: Ratio of the number of 50 paisa, 25 paisa and 10 paisa coins = 5 : 8 : 3 Ratio of their values $\begin{aligned} = \frac{5}{8} : \frac{8}{4} : \frac{3}{10} \\ LCM of 2, 4 and 10 = 20 \\ = (\frac{5}{2} \times 20) : (\frac{8}{4} \times 20) : (\frac{3}{10} \times 20) \\ = 50 : 40 : 6 \\ Sum of the terms of ratio \\ = 50 + 40 + 6 = 96 \\ ∴ Value of 50 paisa coins \\ = \frac{50}{96} \times 144 = 75 \\ ∴ Number of 50 paisa coins \\ = 75 \times 2 = 150 \end{aligned}$

34.

If $x = \frac{1}{3} y$ ÃÂÃÂ and $y = \frac{1}{2} z,$ ÃÂÃÂ then x : y : z is equal to = ?

(A) 3 : 2 : 1
(B) 1 : 2 : 6
(C) 1 : 3 : 6
(D) 2 : 4 : 6

Solution: $\begin{aligned} x = \frac{1}{3} y and y = \frac{1}{2} z \\ \frac{x}{y} = \frac{1}{3} and \frac{y}{z} = \frac{1}{2} \\ x : y = 1 : 3 \\ y : z = 1 : 2 \times 3 (multiply) \\ i . e . y : z = 3 : 6 \\ ∴ x : y : z = 1 : 3 : 6 \end{aligned}$

35.

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

36.

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

37.

Rs. 730 were divided among A,B,C in such a way that if A gets Rs. 3 then B gets Rs. 4 and If B gets Rs. 3.5 then C gets Rs. 3. The share of B exceeds that of C by = ?

(A) Rs. 30
(B) Rs. 40
(C) Rs. 70
(D) Rs. 210

38.

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

(A) 20 : 66 : 95
(B) 21 : 66 : 96
(C) 21 : 66 : 92
(D) 19 : 66 : 92

39.

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: $\begin{matrix} Rs . 1 & : & 50 Paise & : & 25 Paise \\ Value of coins & 8 x & : & 4 x & : & 3 x \\ Number of coins & 8 x \times 1 & : & 4 x \times 2 & : & 3 x \times 4 \\ 8 x & : & 8 x & : & 12 x \end{matrix}$ ∴ Total coins ⇒ 8x + 8x + 12x = 28x 28x = 280 (Given) x = $\frac{280}{28}$ = 10 ∴ Number of 50 paise coins are = 8x = 8 × 10 = 80

40.

In a certain company, the ratio of the number of managers to the number of production - line workers is 5 to 72. If 8 additional production - line workers were to be hired, the ratio of the number of managers to the production - line workers would be 5 to 74. How many managers does the company have ?

(A) 10
(B) 20
(C) 25
(D) 30

Solution: Let the number of managers and production - line workers be 5x and 72x respectively Then, $\begin{aligned} = \frac{5 x}{72 x + 8} = \frac{5}{74} \\ \Rightarrow 370 x = 360 x + 40 \\ \Rightarrow 10 x = 40 \\ \Rightarrow x = 4. \end{aligned}$ ∴ Number of managers = 5 × 4 = 20

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Practice MCQ Questions and Answer on Ratio

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