Practice MCQ Questions and Answer on Ratio

151.

Ratio of earnings of A and B is 8 : 9 respectively. If the earnings of A increase by 50% and the earnings of B decrease by 25%, the new ratio of their earnings becomes 16 : 9 respectively. What are A's earnings?

(A) Rs. 22000
(B) Rs. 28500
(C) Rs. 37000
(D) Cannot be determine

Solution: Let the earnings of A and B Rs. 8x and Rs. 9x respectively. Then, $\begin{aligned} = \frac{150 % of 8 x}{75 % of 9 x} = \frac{16}{9} \\ \Rightarrow \frac{\frac{3}{2} \times 8 x}{\frac{3}{4} \times 9 x} = \frac{16}{9} \\ \Rightarrow \frac{16}{9} = \frac{16}{9} \end{aligned}$ Hence, A's earnings cannot be determined

152.

A sum of Rs. 46,800 is divided among A, B, C and D in such a way that the ratio of the combined share of A and D to the combined share of B and C is 8 : 5. The ratio of the share of B to that of C is 5 : 4. A receives Rs. 18,400. If x is the difference between the share of A and B and y is the difference between the share of C and D, then what is the value of (x - y) (in Rs.)?

(A) 5000
(B) 6000
(C) 7000
(D) 6500

Solution: $\begin{aligned} A + B + C + D = 46800 \\ \frac{A + D}{B + C} = \frac{8}{5} \\ \frac{B}{C} = \frac{5 P}{4 P}, B + C = 9 P \\ \frac{A + D}{9 P} = \frac{8}{5} \\ A + D = \frac{72}{5} P \\ \frac{72}{5} P + 9 P = 46800 \\ 117 P = 46800 \times 5 \\ P = 2000 \\ B = 5 P = 5 \times 2000 = 10000 \\ C = 4 P = 4 \times 2000 = 8000 \\ A = 18400 \\ D = 46800 - 10000 - 8000 - 18400 = 10400 \\ A - B = x = 18400 - 10000 = 8400 \\ D - C = y = 10400 - 8000 = 2400 \\ x - y = 8400 - 2400 = 6000 \end{aligned}$

153.

If a : b = c : d, then $\frac{ma + nc}{mb + nd}$ ÃÂÃÂ is equal to -

(A) m : n
(B) dm : cn
(C) an : mb
(D) a : b

Solution: $\begin{aligned} Let \frac{a}{b} = \frac{c}{d} = k \\ Then, \\ \Rightarrow a = b k, c = d k \\ ∴ \frac{m a + n c}{m b + n d} \\ = \frac{m b k + n d k}{m b + n d} \\ = \frac{k (m b + n d)}{(m b + n d)} \\ \Rightarrow k = \frac{a}{b} \\ \Rightarrow a : b \end{aligned}$

154.

In a college the students in Arts and commerce faculties were in the ratio of 4 : 5 respectively. When 65 more students joined commerce faculty the ratio becomes 8 : 11 respectively. How many students are there in Arts faculty?

(A) 520
(B) 650
(C) 715
(D) Cannot be determined

Solution: Let the number of students in Arts and Commerce faculties be 4x and 5x respectively. Then, $\begin{aligned} = \frac{4 x}{5 x + 65} = \frac{8}{11} \\ \Rightarrow 44 x = 8 (5 x + 65) \\ \Rightarrow 4 x = 520 \\ \Rightarrow x = 130 \end{aligned}$ ∴ Number of students in Arts faculty = (4 × 130) = 520

155.

If 20% of A = 30% of B = $\frac{1}{6}$ of C, then A : B : C is -

(A) 2 : 3 : 6
(B) 3 : 2 : 16
(C) 10 : 15 : 18
(D) 15 : 10 : 18

Solution: $\begin{aligned} 20 % of A = 30 % of B = \frac{1}{6} of C \\ \Rightarrow \frac{20 A}{100} = \frac{30 B}{100} = \frac{C}{6} \\ \Rightarrow \frac{A}{5} = \frac{3 B}{10} = \frac{C}{6} = k (s a y) \\ \Rightarrow A = 5 K, B = \frac{10 k}{3}, C = 6 k \\ ∴ A : B : C = 5 k : \frac{10 k}{3} : 6 k \\ = 5 : \frac{10}{3} : 6 \\ = 15 : 10 : 18 \end{aligned}$

156.

The ratios of copper to zinc in alloys A and B are 3 : 4 and 5 : 9, respectively. A and B are taken in the ratio 2 : 3 and melted to form a new alloy C. What is the ratio of copper to zinc in C?

(A) 3 : 5
(B) 8 : 15
(C) 9 : 11
(D) 27 : 43

Solution: $\begin{aligned} A \to 3 : 4 = 7_{\times 2 \times 2} \\ B \to 5 : 9 = 14_{\times 3} \\ Copper : Zinc \\ 12 : 16 \\ 15 : 27 \\ \overset{―}{27 : 43} \end{aligned}$

157.

A person divided Rs. 10800 among his three sons in the ratio 3 : 4 : 5. Second son kept Rs. 1000 for himself, gave Rs. 600 to his wife and divided the remaining money among his two daughters in the ratio 11 : 9. Then one of his daughters received.

(A) Rs. 1000
(B) Rs. 1050
(C) Rs. 1100
(D) Rs. 1150

Solution: $\begin{aligned} Second son's share \\ = Rs . (10800 \times \frac{4}{12}) \\ = Rs . 3600 \end{aligned}$ Money distributed between the two daughters = Rs. [3600 - (1000 + 600)] = Rs. 2000 $\begin{aligned} First daughter's share \\ = Rs . (2000 \times \frac{11}{20}) \\ = Rs .1100 . \\ Second daughter's share \\ = Rs . (2000 \times \frac{9}{20}) \\ = Rs . 9 00 \end{aligned}$

158.

If p : q : r = 1 : 2 : 4, then $\sqrt{5 p^{2} + q^{2} + r^{2}}$ ÃÂÃÂ ÃÂÃÂ is equal to =

(A) 5
(B) 2q
(C) 5p
(D) 4r

Solution: $\begin{aligned} p : q : r \\ 1 : 2 : 4 \\ x : 2 x : 4 x \\ ∴ \sqrt{5 p^{2} + q^{2} + r^{2}} \\ = \sqrt{5 x^{2} + 4 x^{2} + 16 x^{2}} \\ = \sqrt{25 x^{2}} \\ = 5 x \\ = 5 p \end{aligned}$

159.

If a : b = b : c, then a⁴ : b⁴ is equal to = ?

(A) ac : b2
(B) a2 : c2
(C) c2 : a2
(D) b2 : ac

Solution: $\begin{aligned} a : b = b : c \\ \frac{a}{b} = \frac{b}{c} \\ b^{2} = a c \\ b^{4} = a^{2} c^{2} \\ ∴ a^{4} : b^{4} = \frac{a^{4}}{b^{4}} \\ = \frac{a^{4}}{a^{2} c^{2}} \\ = \frac{a^{2}}{c^{2}} \\ = a^{2} : c^{2} \end{aligned}$

160.

The number of oranges in three basket are in the ratio 3 : 4 : 5. In which ratio the no. of oranges in first two basket must be increased so that the new ratio becomes 5 : 4 : 3 ?

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

Solution: Let, B1 : B2 : B3 = 3x : 4x : 5x and B1 : B2 : B3 = 5y : 4y : 3y Number of oranges remain constant in third basket as increase in oranges takes place only in first two baskets. Hence, 5x = 3y x = $\frac{3 y}{5}$ and, ∴ 3x : 4x : 5x (putting the vale of x) = $\frac{9 y}{5} : \frac{12y}{5} : \frac{15y}{5}$ = 9y : 12y : 15y And, 5y : 4y : 3y (multiple by 5) → 25y : 20y : 15y ∴Increment in first basket = 16 And, Increment in second basket = 8 Thus, Required ratio = $\frac{16}{8}$ = 2 : 1

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Practice MCQ Questions and Answer on Ratio

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