Practice MCQ Questions and Answer on Ratio

31.

The ratio of the first and second class fares between two railway stations is 4 : 1 and that of the number of passengers travelling by first and second classes is 1 : 40. If on a day Rs. 1100 are collected as total fare, the amount collected from the first class passengers is = ?

(A) Rs. 315
(B) Rs. 275
(C) Rs. 137.50
(D) Rs. 100

Solution: 1st : 2nd Fare 4x : x Passengers 1 : 40 Total fare = 4x : 40x = 44x ⇒ 44x = 1100 ⇒ x = $\frac{1100}{44}$ = 25 ∴ Fare = 1st class amount received per day ⇒ 4x = 4 × 25 ⇒ 4x = 100

32.

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

33.

A bucket contains a mixture of two liquids A and B in the proportion 7 : 5. If 9 litres of mixture is replaced by 9 liters of liquid B, then the ratio of the two liquids becomes 7 : 9. How much of the liquid A was there in the bucket ?

(A) 21 liters
(B) 23 liters
(C) 25 liters
(D) 27 liters

Solution: Suppose the can initially contains 7x and 5x litres of mixtures A and B respectively. When 9 litres of mixture are drawn off, quantity of A in mixture left: $\begin{aligned} = [7 x - \frac{7}{12} \times 9] litres \\ = [7 x - \frac{21}{4}] litres \\ Similarly quantity of B in mixture left, \\ = [5 x - \frac{5}{12} \times 9] litres \\ = [5 x - \frac{15}{4}] litres \\ ∴ ratio becomes, \\ \frac{7 x - \frac{21}{4}}{(5 x - \frac{15}{4}) + 9} = \frac{7}{9} \\ \Rightarrow \frac{28 x - 21}{20 x + 21} = \frac{7}{9} \\ \Rightarrow 252 x - 189 = 140 x + 147 \\ \Rightarrow 112 x = 336 \\ \Rightarrow x = 3 \\ So the can contained, \\ = 7 \times x \\ = 7 \times 3 \\ = 21 litres of A initially . \end{aligned}$

34.

At a casino in Mumbai, there are 3 tables A, B and C. The payoffs at A is 10 : 1, at B is 20 : 1 and C is 30 :1. If a man bets Rs. 200 at each table and win at two of the tables, what is the maximum and minimum difference between his earnings can be ?

(A) Rs. 4000
(B) Rs. 4500
(C) Rs. 2500
(D) Rs. 2000

35.

The falling height of an object is proportional to the square of the time. One object falls 64 cm in 2 sec then in 6 sec from how much height the object will fall ?

(A) 192 cm
(B) 276 cm
(C) 436 cm
(D) 576 cm

36.

The ratio between the third proportional of 12 and 30 and mean proportional of 9 and 25 is -

(A) 2 : 1
(B) 5 : 1
(C) 7 : 15
(D) 9 : 14

Solution: Let the third proportional to 12 and 30 be x. Then, $\begin{aligned} = 12 : 30 :: 30 : x \\ \Rightarrow 12 x = 30 \times 30 \\ \Rightarrow x = \frac{(30 \times 30)}{12} = 75 \end{aligned}$ ∴ Third proportional to 12 and 30 = 75 Mean proportional between 9 and 25 $\begin{aligned} = \sqrt{9 \times 25} = 15 \\ ∴ Required ratio = 75 : 15 \\ = 5 : 1 \end{aligned}$

37.

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

38.

A mixture contains spirit and water in the ratio of 3 : 2. If it contains 3 litres more spirit than water, the quantity of spirit in the mixture is = ?

(A) 12 litres
(B) 10 litres
(C) 9 litres
(D) 8 litres

39.

A mixture contains milk and water in the ratio 5 : 1. On adding 5 litres of water, the ratio of milk and water becomes 5 : 2. The quantity of milk in the mixture is = ?

(A) 16 litres
(B) 25 litres
(C) 32.5 litres
(D) 22.75 litres

40.

Salaries of B, C, D and E are in the ratio of 2 : 3 : 4 : 5 respectively. Their salaries are increased by 20 percent, 30 percent, 40 percent and 50 percent respectively. If the increased salary of D is Rs. 560, then what is the sum of the original salaries of B, C, D and E?

(A) Rs. 1820
(B) Rs. 1400
(C) Rs. 1560
(D) Rs. 1260

Solution: If salary of D = 4m 4m + 0.4(4m) = 560 4m + 1.6m = 560 m = $\frac{560}{5.6}$ m = 100 Original salary of B, C, D, E = 2m + 3m + 4m + 5m = 14m = 14 × 100 = 1400 Hence, the sum of the original salaries of B, C, D and E is Rs. 1400

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Practice MCQ Questions and Answer on Ratio

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