Practice MCQ Questions and Answer on Alligation

41.

The milk and water in a mixture are in the ratio 7 : 5. When 15 litres of water are added to it. The ratio of milk and water in the new mixture becomes 7 : 8. The total quantity of water in the new mixture is -

(A) 35 litres
(B) 40 litres
(C) 60 litres
(D) 96 litres

Solution: According to the question, $Milk : Water$ $\begin{matrix} 7 : 5 \\ 7 : 8 \end{matrix}) 3 unit$ ∴ Remember water is added and not milk, so make milk equal but here milk is already equal $\begin{aligned} 3 units = 15 litres \\ 1 unit = 5 litres \\ 8 units = 40 litres \end{aligned}$ Total quantity of water in the new mixture = 40 litres

42.

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

43.

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

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

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

44.

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

45.

The acid and water in two vessels A and B are in the ratio 4 : 3 and 2 : 3. In what ratio should the liquid in both the vessels be mixed to obtain a new mixture in vessel C containing half acid and half water ?

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

Solution: According to the question, $\begin{aligned} Acid Water \\ Vessel A 4 : 3 \\ Vessel B 2 : 3 \end{aligned}$ Now using alligation,

46.

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.

47.

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%

48.

A vessel contains 60 litre of milk. 12 litres of milk taken out from it and replaced with water. Then again from mixture, 12 litres is taken out and replaced with water. The ratio of milk and water in the resultant mixture is ?

(A) 16 : 9
(B) 15 : 10
(C) 16 : 10
(D) 9 : 5

Solution: Total milk = 60 litresDrawn off = 12 litres $\frac{Final quantity}{Initial quantity}$ $= {(1 - \frac{x}{c})}^{t}$ X = Replaced quantity C = Capacity T = Number of process $\begin{aligned} \frac{Final quantity}{Initial quantity} = {(1 - \frac{12}{60})}^{2} \\ = {(\frac{4}{5})}^{2} \\ = \frac{16}{25} \end{aligned}$ Ratio of milk and water in the resultant mixture : = 16 : 9

49.

Wheat worth Rs. 80 per kg and Rs. 50 per kg is mixed with a third variety in the ratio 1 : 2 : 3. If the mixture is worth Rs. 75 per kg, then the price of the third variety per kg will be equal to:

(A) Rs. 95
(B) Rs. 85
(C) Rs. 80
(D) Rs. 90

Solution: $\begin{aligned} Let third variety = x \\ 80 : 50 : x \\ 1 : 2 : 3 \\ \overset{―}{80 + 100 + 3 x} = (3 + 2 + 1) \times 75 \\ 180 + 3 x = 6 \times 75 \\ 3 x = 270 \\ x = 90 per kg \end{aligned}$

50.

The ratio of milk and water in mixture of four containers are 5 : 3, 2 : 1, 3 : 2 and 7 : 4 respectively. In which container is the quantity of milk, relative to water, minimum ?

(A) First
(B) Second
(C) Third
(D) Forth

Solution: ∴According to the question,Container : $\begin{aligned} I II III IV \\ M : W M : W M : W M : W \\ 5 : 3 2 : 1 3 : 2 7 : 4 \end{aligned}$ $\begin{aligned} C o n t a i n e r (I) : \\ \frac{Milk}{Water} = \frac{5}{3} = 1.67 \\ C o n t a i n e r (II) : \\ \frac{Milk}{Water} = \frac{2}{1} = 2 \\ C o n t a i n e r (III) : \\ \frac{Milk}{Water} = \frac{3}{2} = 1.5 \\ C o n t a i n e r (IV) : \\ \frac{Milk}{Water} = \frac{7}{4} = 1.75 \end{aligned}$ ∴ The quantity of milk relative to water minimum in container third.

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Practice MCQ Questions and Answer on Alligation

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