Practice MCQ Questions and Answer on Alligation

Three vessels whose capacities are in the ratio of 3 : 2 : 1 are completely filled with milk mixed with water. The ratio of milk and water in the mixture of vessels are 5 : 2, 4 : 1 and 4 : 1 respectively. Taking $\frac{1}{3}$ of first, $\frac{1}{2}$ of second and $\frac{1}{7}$ of third mixture, a new mixture kept in a new vessel is prepared. The percentage of water in the new mixture is -

(A) 32%
(B) 28%
(C) 30%
(D) 24%

Solution: Capacities of vessels $3 : 2 : 1$ $\begin{aligned} M : W T Mixture \\ V - 1 \to (5 : 2 = 7)_{\times 5} \\ V - 2 \to (4 : 1 = 5)_{\times 7} \\ V - 3 \to (4 : 1 = 5)_{\times 7} \end{aligned}$ Equate the mixture $\begin{aligned} M : W T Mixture \\ (V - 1) \to 25 : 10 = 35 \\ (V - 2) \to 28 : 7 = 35 \\ (V - 3) \to 28 : 7 = 35 \end{aligned}$ $\begin{aligned} Capacities M : W = Total Mix . \\ (V - 1) \times 3 \to 75 : 30 = 105 \\ (V - 2) \times 2 \to 56 : 14 = 70 \\ (V - 1) \times 1 \to 28 : 7 = 35 \end{aligned}$ Water taken out $\Rightarrow \frac{1}{3} of water in (V - 1)$ $+ \frac{1}{2} of water in (V - 2)$ $+ \frac{1}{7} of water in (V - 3)$ $\begin{aligned} \Rightarrow \frac{1}{3} \times 30 + \frac{1}{2} \times 14 + \frac{1}{7} \times 7 \\ \Rightarrow 10 + 7 + 1 \\ \Rightarrow 18 \end{aligned}$ Similarly mixture will be $\Rightarrow \frac{1}{3} \times 105 + \frac{1}{2} \times 70 + \frac{1}{7}$ × 35 ⇒ 75 $\begin{aligned} ∴ % of water = \frac{18}{75} \times 100 \\ = 24 % \end{aligned}$

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

In 2 kg mixture of copper and aluminium, 30% is copper. How much aluminium powder should be added to the mixture so that the quantity of copper becomes 20% ?

(A) 900 gms
(B) 800 gms
(C) 1000 gms
(D) 1200 gms

Solution: According to the question, Mixture of copper and aluminium = 2000 gms 30% is copper means = $\frac{30}{100}$ × 2000 = 600 gms copper $\begin{aligned} \Rightarrow \frac{600}{1400 + x} = \frac{20 %}{80 %} \\ \Rightarrow 1400 + x = 2400 \end{aligned}$ ⇒ x = 1000 gms

In 80 litres mixture of milk and water the ratio of amount of milk to that of amount of water is 7 : 3. In order to make this ratio 2 : 1, how many litres of water should be added ?

(A) 5 litres
(B) 6 litres
(C) 8 litres
(D) 4 litres

Solution: According to the question, $\begin{aligned} Milk : Water \\ Initial Ratio 7_{\times 2} : 3_{\times 2} \\ Final Ratio 2_{\times 7} : 1_{\times 7} \end{aligned}$ ∴ Remember water is added not milk, so make milk equal $\begin{matrix} M : W \\ \begin{matrix} Initial 14 : 6 \\ Final 14 : 7 \end{matrix}) \end{matrix}$ $\begin{aligned} = 20 unit \\ 1 \end{aligned}$ $\begin{aligned} 20 units = 80 litres \\ 1 unit = 4 litres \\ Water added = 4 litres \end{aligned}$

A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?

(A) 4 litres, 8 litres
(B) 6 litres, 6 litres
(C) 5 litres, 7 litres
(D) 7 litres, 5 litres

Solution: Let the cost of 1 litre milk be Rs. 1 Milk in 1 litre mixture in 1st can = $\frac{3}{4}$ litre, C.P. of 1 litre mixture in 1st can Rs. $\frac{3}{4}$ Milk in 1 litre mixture in 2nd can = $\frac{1}{2}$ litre, C.P. of 1 litre mixture in 2nd can Rs. $\frac{1}{2}$ Milk in 1 litre of final mixture = $\frac{5}{8}$ litre, Mean price = Rs. $\frac{5}{8}$ By the rule of alligation, we have: ∴ Ratio of two mixtures = $\frac{1}{8}$ : $\frac{1}{8}$ = 1 : 1 So, quantity of mixture taken from each can = $(\frac{1}{2} \times 12)$ = 6 litres

The price of a variety of a commodity is Rs. 7 per kg and that of another is Rs. 12 per kg. Find the ratio in which two varieties should be mixed so that the price of the mixture is Rs. 10 per kg.

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

40 litres of 60% concentration of acid solution is added to 35 litres of 80% concentration of acid solution. What is the concentration of acid in the new solution?

(A) 66%
(B) $66 \frac{2}{3} %$
(C) $69 \frac{1}{3} %$
(D) 69%

Solution: $\begin{aligned} I \to \frac{40 \times 60}{100} = 24 \\ II \to \frac{35 \times 80}{100} = 28 \\ Acid % = \frac{52}{75} \times 100 = 69 \frac{1}{3} % \end{aligned}$

60 kg of an alloy A is mixed with 100 kg of alloy B. If alloy A has lead and tin in the ratio 3 : 2 and alloy B has tin and copper in the ratio 1 : 4, the amount of tin in the new alloy is -

(A) 44 kg
(B) 53 kg
(C) 80 kg
(D) 24 kg

Solution: Quantity of tin in 60 kg of A $\begin{aligned} = (60 \times \frac{2}{5}) kg \\ = 24 kg \end{aligned}$ Quantity of tin in 100 kg of B $\begin{aligned} = (100 \times \frac{1}{5}) kg \\ = 20 kg \end{aligned}$ ∴ Quantity of tin in the new alloy = (24 + 20) kg = 44 kg

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

10.

Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg.

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

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Practice MCQ Questions and Answer on Alligation

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