Practice MCQ Questions and Answer on Alligation

51.

How many kg of salt costing Rs. 28 per kg must be mixed with 39.6 kg of salt costing Rs. 16 per kg, so that selling the mixture at Rs. 29.90, there is a gain of 15%.

(A) 198
(B) 135
(C) 132
(D) 131

52.

The ratio of milk to water in a 100 litres mixture is 2 : 3. 10 litres of this mixture is withdrawn and replaced with milk. This process is repeated 2 more times. What is the percentage of milk in final mixture?

(A) 58.21%
(B) 51.24%
(C) 54.27%
(D) 56.26%

Solution: $\begin{matrix} Milk & Water \\ \begin{matrix} 2 \\ ↓ \end{matrix} & \begin{matrix} : \end{matrix} & \begin{matrix} 3 \\ ↓ \end{matrix} & \begin{matrix} = 5 \to 100 \\ 1 \to 20 \end{matrix} \\ 40 & 60 \end{matrix}$ $\begin{aligned} = 60 {(1 - \frac{10}{100})}^{3} % \\ = 60 {(\frac{9}{10})}^{3} % \\ = 60 \times \frac{729}{1000} % \\ = 43.74 % \\ ∴ Final milk % = (100 - 43.74) % \\ = 56.26 % \end{aligned}$

53.

Weights of two friends Ram and Shyam are in the ratio 4 : 5. If Ram's weight is increased by 10% and total weight of Ram and Shyam become 82.8 kg, with an increases of 15%. By what percent did the weight of Shyam has to be increased?

(A) 19%
(B) 10%
(C) 21%
(D) 16%

Solution: Now, given ratio of Ram and Shayam's weight = 4 : 5 Hence, $\frac{x - 15}{15 - 10} = \frac{4}{5}$ Or, x = 19%

54.

A mixture of milk and water measures 60 litres. It contains 10% water. How much water should be added to it, so that the water may be 25%?

(A) 18 litres
(B) 14 litres
(C) 16 litres
(D) 12 litres

Solution: $\begin{matrix} 10 % & 100 % \\ 25 % \\ 75 % & 15 % \\ 60 \leftarrow 5 & : & 1 \to 12 litres \end{matrix}$

55.

A milkman has a 15 litres drum with 9 litres milk. He filled the drum with water and now takes out $\frac{1}{2}$ litre of the mixture. What is the quantity of milk (in millilitres) in the mixture taken out?

(A) 250
(B) 266
(C) 300
(D) 333

Solution: $\begin{matrix} Total capacity & Milk & Water \\ 15 & 9 & : & 6 \\ 3 & : & 2 \end{matrix}$ Half liter is taken out Milk = 500 ml × $\frac{3}{5}$ = 300 ml

56.

A mixture of a certain quantity of milk with 16 litres of water is worth 90 paise per litre. If pure milk be worth Rs. 1.80 per litre. How much milk is there in the mixture ?

(A) 40 litres
(B) 16 litres
(C) 60 litres
(D) 80 litres

57.

In a zoo, there are deers and ducks. If the heads are counted, there are 180, while the legs are 448. What will be the number of deers in the zoo?

(A) 136
(B) 68
(C) 44
(D) 22

Solution: Average legs per head = $\frac{448}{180}$ Deers : Ducks = 88 : 272 Hence, the number of Deers = $\frac{180 \times 88}{360}$ = 44

58.

The respective ratio of milk and water in the mixture is 4 : 3. If 6 litres of water is added to this mixture, the respectively ratio of milk and water becomes 8 : 7. What is the quantity of milk in the original mixture ?

(A) 36 litres
(B) 84 litres
(C) 48 litres
(D) None of these

Solution: Let the quantity of milk and water in initial mixture be 4x and 3x litres. Quantity of water = 3x litres On adding 6 litres of water, we get $\begin{aligned} \Rightarrow \frac{4 x}{3 x + 6} = \frac{8}{7} \\ \Rightarrow 28 x = 24 x + 48 \\ \Rightarrow 28 x - 24 x = 48 \\ \Rightarrow 4 x = 48 \\ \Rightarrow x = \frac{48}{4} \\ \Rightarrow x = 12 \end{aligned}$ ∴ Required quantity of milk = 4x = 4 × 12 = 48 litres

59.

Two blends of a commodity costing Rs. 35 and Rs. 40 per kg respectively are mixed in the ratio 2 : 3 by weight. If one-fifth of the mixture is sold at Rs. 46 per kg and the remaining at the rate Rs. 55 per kg, the profit percent is -

(A) 50%
(B) 20%
(C) 40%
(D) 30%

Solution: Let first blend is 2 kg and second blend is 3 kg. $\begin{aligned} Total cost price \\ = (35 \times 2) + (40 \times 3) \\ = 70 + 120 \\ = Rs . 190 \\ Total selling price \\ = (1 \times 46) + (4 \times 55) \\ = 266 [\frac{1}{5} of 5kg = 1kg] \\ ∴ Profit percent \\ \Rightarrow \frac{Total profit}{Total cost price} \times 100 \\ \Rightarrow \frac{(266 - 190)}{190} \times 100 \\ \Rightarrow \frac{76}{190} \times 100 \\ \Rightarrow 40 % \end{aligned}$

60.

12500 students appeared in an exam. 50% of the boys and 70% of the girls cleared the examination. If the total percent of student qualifying is 60% , how many girls appeared in the exam ?

(A) 6500
(B) 6200
(C) 5500
(D) 6250

Solution: $\begin{aligned} Number of girls \\ = \frac{1}{2} \times 12500 \\ = 6250 \end{aligned}$

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Practice MCQ Questions and Answer on Alligation

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