Practice MCQ Questions and Answer on Ratio

141.

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

142.

Divide Rs. 671 among A, B and C such that if their shares be increased by Rs. 3, Rs. 7 and Rs. 9 respectively the remainder shall be in the ratio 1 : 2 : 3.

(A) Rs. 110, Rs. 220, Rs. 336
(B) Rs. 112, Rs. 223, Rs. 336
(C) Rs. 105, Rs. 223, Rs. 330
(D) None of these

Solution: $\begin{aligned} Remainder \\ = Rs . [671 + (3 + 7 + 9)] \\ = Rs . 690 \\ A's share \\ = Rs . [(690 \times \frac{1}{6}) - 3] \\ = Rs . 112 \\ B's share \\ = Rs . [(690 \times \frac{2}{6}) - 7] \\ = Rs . 223 \\ C's share \\ = Rs . [(690 \times \frac{3}{6}) - 9] \\ = Rs . 336 \end{aligned}$

143.

Last year, the ratio between the salaries of A and B was 3 : 4. But the ratios of their individual salaries between last year and this year were 4 : 5 and 2 : 3 respectively. If the sum of their present salaries is Rs. 4160, then how much is the salary of A now ?

(A) Rs. 1040
(B) Rs. 1600
(C) Rs. 2560
(D) Rs. 3120

Solution: let the salaries of A and B last year be Rs. 3x and Rs. 4x respectively. Then, $\begin{aligned} A's present salary \\ = Rs . (\frac{5}{4} \times 3 x) \\ = Rs . (\frac{15 x}{4}) \\ B's present salary \\ = Rs . (\frac{3}{2} \times 4 x) \\ = Rs .6 x . \\ ∴ \frac{15 x}{4} + 6 x = 4160 \\ \Rightarrow 39 x = 4160 \times 4 \\ \Rightarrow x = \frac{4160 \times 4}{39} \\ So, \\ A's present salary \\ = Rs . (\frac{15}{4} \times \frac{4160 \times 4}{39}) \\ = Rs .1600 \end{aligned}$

144.

If a : b = b : c, then a⁴ : b⁴ would be equal to

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

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

145.

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

146.

In a colored picture of blue and yellow color, blue and yellow color is used in the ratio of 4 : 3 respectively. If in the upper half, half blue : yellow is 2 : 3, then in the lower half blue : yellow is =?

(A) 1 : 1
(B) 2 : 1
(C) 26 : 9
(D) 9 : 26

Solution: Given, blue and yellow color ratio = 4 : 3 and half part blue and yello ratio = 2 : 3 Let 700 be the painting part in total ∴ Blue part will be: $\frac{4}{7} \times 700$ = 400 And yellow will be: $\frac{3}{7} \times 700$ = 300 Now, upper half part i.e $\frac{700}{2}$ = 350 Blue in upper half part → $\frac{2}{5} \times 350$ = 140 And, Yellow in upper half part → $\frac{3}{5} \times 350$ = 210 Remaining half Blue in lower part → 400 - 140 = 260 Remaining half yellow in lower part → 300 - 90 = 210 Ratio of blue and yellow → 260 : 90 ⇒ 26 : 9

147.

If a : b = 5 : 7 and c : d = 2a : 3b then ac : bd is = ?

(A) 20 : 38
(B) 50 : 147
(C) 10 : 21
(D) 50 : 151

Solution: $\begin{aligned} a : b c : d \\ 5 : 7 2 a : 3 b \\ \frac{a}{b} = \frac{5}{7}, \frac{c}{d} = \frac{2 a}{3 b} \\ = \frac{2}{3} \times \frac{5}{7} \\ = \frac{10}{21} \\ ∴ a c : b d \\ = \frac{ac}{bd} \\ = \frac{5}{7} \times \frac{10}{21} \\ = \frac{50}{147} \\ = 50 : 147 \end{aligned}$

148.

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: $\begin{aligned} p = k, q = 2 k, r = 4 k \\ Then, \\ \sqrt{5 p^{2} + q^{2} + r^{2}} \\ = \sqrt{5 k^{2} + {(2 k)}^{2} + {(4 k)}^{2}} \\ = \sqrt{5 k^{2} + 4 k^{2} + 16 k^{2}} \\ = \sqrt{25 k^{2}} \\ = 5 k \\ = 5 p . \end{aligned}$

149.

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

150.

The ratio of the incomes of Ram and Shyam is 7 : 17 and that of Shyam and Sohan is 7 : 17. If the income of Ram is Rs. 490, what is the income of Sohan ?

(A) Rs. 490
(B) Rs. 1190
(C) Rs. 2790
(D) Rs. 2890

Solution: $\begin{aligned} Ram : Shyam = 7 : 17 \\ Shyam : Sohan = 7 : 17 \\ = (7 \times \frac{17}{7}) : (17 \times \frac{17}{7}) \\ = 17 : \frac{289}{7} \\ Ram : Shyam : Sohan \\ = 7 : 17 : \frac{289}{7} \\ = 49 : 119 : 289 \end{aligned}$ Let Sohan's income be Rs. x Then, = 49 : 289 :: 490 : x or x = 2890

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Practice MCQ Questions and Answer on Ratio

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