Practice MCQ Questions and Answer on Alligation

11.

A sugar solution of 3 litres contain 60% sugar. One litre of water is added to this solution. Then the percentage of sugar in the new solution is :-

(A) 30%
(B) 45%
(C) 50%
(D) 60%

Solution: Percentage of sugar in 4 litres mixture. $\begin{aligned} = \frac{9}{5 \times 4} \times 100 \\ = 45 % \end{aligned}$

12.

If X beakers of 100 ml containing 1 : 4 acid-water solution are mixed with Y beakers of 200 ml containing 3 : 17 acid-water solution then the ratio of acid to water in the resulting mixture becomes 19 : 91. Find X : Y.

(A) 5 : 3
(B) 3 : 5
(C) 7 : 13
(D) 13 : 7

13.

The ratio of milk to water in a 100 litres mixture is 2 : 3. 10 litres of this mixture is withdrawn and replaced with milk.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: $\begin{matrix} Milk & Water \\ \begin{matrix} 2 \\ ↓ \end{matrix} & \begin{matrix} : \end{matrix} & \begin{matrix} 3 \\ ↓ \end{matrix} & \begin{matrix} = 5 \to 100 \\ 1 \to 20 \end{matrix} \\ 40 & 60 \end{matrix}$ $\begin{aligned} = 60 {(1 - \frac{10}{100})}^{3} % \\ = 60 {(\frac{9}{10})}^{3} % \\ = 60 \times \frac{729}{1000} % \\ = 43.74 % \\ ∴ Final milk % = (100 - 43.74) % \\ = 56.26 % \end{aligned}$

14.

Nikita bought 30 kg of wheat at the rate of Rs. 9.50 per kg and 40 kg of wheat at the rate of Rs. 8.50 per kg and mixed them. She sold the mixture at the rate of Rs. 8.90 per kg. Her total profit or loss in the transaction was -

(A) Rs. 2 loss
(B) Rs. 2 profit
(C) Rs. 7 loss
(D) Rs. 7 profit

15.

In what ratio must tea at Rs. 62 per kg be mixed with tea at Rs. 72 per kg so that the mixture must be worth Rs. 64.50 per kg?

(A) 3 : 1
(B) 3 : 2
(C) 4 : 3
(D) 5 : 3

16.

A trader has 50 kg of pulses, part of which he sells at 14% profit and rest at 6% loss. On the whole his loss is 4%. How much quantity is sold at 14% profit and that at 6% loss?

(A) 5 kg, 45 kg.
(B) 15 kg, 35 kg.
(C) 10kg, 40 kg.
(D) None of these

Solution: Hence, ratio of quantity sold at 14% profit and 6% loss, = 2 : 18 = 1 : 9 Hence, pulses sold at 14% profit, = $\frac{50 \times 1}{10}$ = 5 kg. At 6% Wheat sold at loss = 45 kg.

17.

A vessel contained a solution of acid and water, in which water was 64%. Four litres of the solution was taken out of the vessel and the same quantity of water was added. If the resulting solution contains 30% acid, the quantity (in litres) of the water in the solution, at the beginning in the vessel, was:

(A) 8.64
(B) 15.36
(C) 12.64
(D) 11.36

Solution: $\begin{matrix} Acid & Water \\ Old \to & 36 % & 64 % \\ New \to & 30 % & 70 % \end{matrix}$ $\begin{aligned} Old mixture = Remaining + Taken out \\ = 20 L + 4 L \\ = 24 L \\ Water = 24 \times \frac{64}{100} \Rightarrow 15.36 L \end{aligned}$

18.

A vessel contains milk and water in the ratio 3 : 2. The volume of the contents is increased by 50% by adding water to it. From this resultant solution 30 L is withdrawn and then replaced with water. The resultant ratio of milk water in the final solution is 3 : 7. Find the original volume of the solution.

(A) 80 L
(B) 65 L
(C) 75 L
(D) 82 L

Solution: Let the original volume be x. then, quantity of milk and water, = $\frac{3 x}{5}$ and $\frac{2 x}{5}$ respectively. After adding water to it, the volume becomes 150%, the quantity of milk and water, = $\frac{3 x}{5}$ and $\frac{9 x}{10}$ $\frac{\frac{3 x}{5} - 12}{\frac{9 x}{10} + 12} = \frac{3}{7}$ 14(3x - 60) = 3(9x + 120) Or, x = 80 L

19.

A jar contains a blend of a fruit juice and water in the ratio 5 : x. When 1 litre of water is added to 4 litres of the blend the ratio of fruit juice to water becomes 1 : 1. What is the value of x?

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

20.

The proportion of acid and water in three samples is 2 : 1, 3 : 2 and 5 : 3. A mixture containing equal quantities of all three samples is made. The ratio of water and acid in the mixture is -

(A) 120 : 133
(B) 227 : 133
(C) 227 : 120
(D) 133 : 227

Solution: According to the question, $\begin{matrix} Acid Water Total \\ \begin{matrix} Sample I 2_{\times 40} = 80 : 1_{\times 40} = 40 3_{\times 40} \\ Sample II 3_{\times 24} = 72 : 2_{\times 24} = 48 5_{\times 24} \\ Sample III \underset{―}{5_{\times 15} = 75} : \underset{―}{3_{\times 15} = 45} 8_{\times 15} \end{matrix}] 120 \end{matrix}$ $Ratio of quantity 227 : 133$ $Required ratio = 133 : 227$

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Practice MCQ Questions and Answer on Alligation

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