Alligation - Aptitude MCQ Questions and Solutions with Explanations

21

In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?

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

Discuss

Answer & Solution

Answer: Option C

Solution:

By the rule of alligation, we have:
Alligation mcq solution image

∴ Required rate = 3.50 : 1.50 = 7 : 3

22

A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is:

A) 4% B) 16% C) 20% D) 25%

Discuss

Answer & Solution

Answer: Option C

Solution:

Let C.P. of 1 litre milk be Rs. 1
Then, S.P. of 1 litre of mixture = Rs. 1, Gain = 25%
C.P. of 1 litre mixture = Rs. $$\left( {\frac{{100}}{{125}} \times 1} \right)$$ = $$\frac{4}{5}$$
By the rule of alligation, we have:
Alligation mcq solution image

∴ Ratio of milk to water = $$\frac{4}{5}$$ : $$\frac{1}{5}$$ = 4 : 1
Hence, percentage of water in the mixture = $$\left( {\frac{1}{5} \times 100} \right)$$ % = 20%

23

A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?

A) 26.34 litres B) 27.36 litres C) 28 litres D) 29.16 litres

Discuss

Answer & Solution

Answer: Option D

Solution:

$$\eqalign{ & {\text{Amount}}\,{\text{of}}\,{\text{milk}}\,{\text{left}}\,{\text{after}}\,{\text{3}}\,{\text{operations}} \cr & = \left[ {40{{\left( {1 - \frac{4}{{40}}} \right)}^3}} \right]\,{\text{litres}} \cr & = \left( {40 \times \frac{9}{{10}} \times \frac{9}{{10}} \times \frac{9}{{10}}} \right)\,{\text{litres}} \cr & = 29.16\,{\text{litres}} \cr} $$

24

A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containing 19% alcohol and now the percentage of alcohol was found to be 26%. The quantity of whisky replaced is:

A) $$\frac{{1}}{{3}}$$ B) $$\frac{{2}}{{3}}$$ C) $$\frac{{2}}{{5}}$$ D) $$\frac{{3}}{{5}}$$

Discuss

Answer & Solution

Answer: Option B

Solution:

By the rule of alligation, we have:
Alligation mcq solution image

So, ratio of 1^st and 2^nd quantities = 7 : 14 = 1 : 2
∴ Required quantity replaced = $$\frac{2}{3}$$

25

In what ratio must water be mixed with milk to gain $$16\frac{2}{3}\% $$ on selling the mixture at cost price?

A) 1 : 6 B) 6 : 1 C) 2 : 3 D) 4 : 3

Discuss

Answer & Solution

Answer: Option A

Solution:

Let C.P. of 1 litre milk be Rs. 1
S.P. of 1 litre of mixture = Rs. 1, Gain = $$\frac{50}{3}$$ %
∴ C.P. of 1 litre of mixture = $$ {100 \times \frac{3}{{350}} \times 1} $$ = $$\frac{6}{7}$$
BY the rule of alligation, we have:
Alligation mcq solution image

∴ Ration of water and milk = $$\frac{{1}}{{7}}$$ : $$\frac{{6}}{{7}}$$ = 1 : 6

26

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

Discuss

Answer & Solution

Answer: Option B

Solution:

By the rule of alligation:
Alligation mcq solution image

∴ Required ratio = 60 : 90 = 2 : 3

27

In what ratio must a grocer mix two varieties of tea worth Rs. 60 a kg and Rs. 65 a kg so that by selling the mixture at Rs. 68.20 a kg he may gain 10%?

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

Discuss

Answer & Solution

Answer: Option A

Solution:

S.P. of 1 kg of the mixture = Rs. 68.20, Gain = 10%
C.P. of 1 kg of the mixture = Rs. $$\left( {\frac{{100}}{{110}} \times 68.20} \right)$$ = Rs. 62
By the rule of alligation, we have:
Alligation mcq solution image

∴ Required ratio = 3 : 2

28

The cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs. 20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is:

A) Rs. 18 B) Rs. 18.50 C) Rs. 19 D) Rs. 19.50

Discuss

Answer & Solution

Answer: Option A

Solution:

Let the price of the mixed variety be Rs. x per kg.
By rule of alligation, we have:
Alligation mcq solution image

$$\eqalign{ & \therefore \frac{{20 - x}}{{x - 15}} = \frac{2}{3} \cr & \Rightarrow 60 - 3x = 2x - 30 \cr & \Rightarrow 5x = 90 \cr & \Rightarrow x = 18 \cr} $$

29

8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of water is 16 : 65. How much wine did the cask hold originally?

A) 18 litres B) 24 litres C) 32 litres D) 42 litres

Discuss

Answer & Solution

Answer: Option B

Solution:

Let the quantity of the wine in the cask originally be x litres.
Then, quantity of wine left in cask after 4 operations
$$\eqalign{ & = \left[ {x{{\left( {1 - \frac{8}{x}} \right)}^4}} \right]\,{\text{litres}} \cr & \therefore \left( {{{\frac{{x\left( {1 - \left( {\frac{8}{x}} \right)} \right)}}{x}}^4}} \right) = \frac{{16}}{{81}} \cr & \Rightarrow {\left( {1 - \frac{8}{x}} \right)^4} = {\left( {\frac{2}{3}} \right)^4} \cr & \Rightarrow {\frac{{x - 8}}{x}} = \frac{2}{3} \cr & \Rightarrow 3x - 24 = 2x \cr & \Rightarrow x = 24 \,\text{litres} \cr} $$

30

A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is:

A) 400 kg B) 560 kg C) 600 kg D) 640 kg

Discuss

Answer & Solution

Answer: Option C

Solution:

By the rule of alligation, we have:
Alligation mcq solution image

Ratio of 1^st and 2^nd parts
= 4 : 6
= 2 : 3
∴ Quantity of 2^nd kind
$$\eqalign{ & = \left( {\frac{3}{5} \times 1000} \right)\,{\text{kg}} \cr & = 600\,{\text{kg}} \cr} $$