Practice MCQ Questions and Answer on Alligation

11.

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

12.

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

13.

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 $\begin{aligned} ∴ % of water = \frac{18}{75} \times 100 \\ = 24 % \end{aligned}$

14.

To gain 10% on selling sample of milk at the cost price of pure milk, the quantity of water to be mixed with 50 kg. of pure milk is:

(A) 2.5 kg
(B) 5 kg
(C) 7.5 kg
(D) 10 kg

Solution: 1st Method (Method of Alligation): Let the quantity of water to be mixed is x kg. Let cost of milk be Rs. 1 per kg. Then SP of 50 kg of milk with gain 10% = Rs. 55 [As Cost of 50 kg milk = Rs. 50, then SP = (50 + 10% of 50)] Then, water to be mixed is 5 kg, As the selling price of the milk is Rs. 1 per kg. Seller has to have 10% gain on 50 kg milk, he must have to add 5 kg water to 50 kg milk. 2nd Method (Simple Method): Let the quantity of water mixed be x kg. Let CP of 1 kg of pure milk = Rs. 1. Hence, % gain = x × $\frac{100}{50}$ 10 = $\frac{100 x}{50}$ Or, 2x = 10 or, x = 5 kg.

15.

A mixture contains alcohol and water in the ratio 4 : 3. If 5 litres of water is added to the mixture, the ratio becomes 4 : 5. The quantity of alcohol in the given mixture is -

(A) 3 litres
(B) 4 litres
(C) 15 litres
(D) 10 litres

Solution: Let the quantity of alcohol and water be 4x litres and 3x litres respectively $\begin{aligned} \frac{4 x}{(3 x + 5)} = \frac{4}{5} \\ \Rightarrow 20 x = 4 (3 x + 5) \\ \Rightarrow 8 x = 20 \\ \Rightarrow x = 2.5 \end{aligned}$ Quantity of alcohol = (4 × 2.5) litres = 10 litres.

16.

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

17.

A mixture is composed of 11 parts of pure milk and 2 parts of water. If 35 litres of water were added to the mixture then the new mixture will contain twice as much pure milk as water, then how many litres of pure milk does the original mixture contain?

(A) 110
(B) 55
(C) 220
(D) 70

Solution: $\begin{matrix} Original mixture & Milk & Water \\ 11 & : & 2 \\ 2 & : & 1 \end{matrix}$ So, the quantity of milk in original mixture is 22 unit × 5 Ltr. = 110 Ltr.

18.

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%

19.

An alloy contains copper and tin in the ratio 3 : 2. If 250 gm of copper is added to this alloy then copper in it becomes double the quantity of tin in it. What is the amount (in gm) of tin in the alloy?

(A) 250
(B) 750
(C) 1000
(D) 500

20.

In what ratio must a mixture of 30% alcohol strength be mixed with that of 50% alcohol strength so as to get a mixture of 45% alcohol strength?

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

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Practice MCQ Questions and Answer on Alligation

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