Practice MCQ Questions and Answer on Alligation

21.

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

22.

In two types of stainless steel, the ratio of chromium and steel are 2 : 11 and 5 : 21 respectively. In what proportion should the two types be mixed so that the ratio of chromium to steel in the mixed type becomes 7 : 32 ?

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

Solution: According to the question, $\begin{matrix} Chromium Steel \\ Type 1 2 : 11 \\ Type 2 5 : 21 \end{matrix}$ Now using alligation, $Ratio of quantity \to 1 : 2$

23.

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

24.

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

25.

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

26.

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

27.

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.

28.

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

Solution: S.P. of 1 kg of the mixture = Rs. 68.20, Gain = 10% C.P. of 1 kg of the mixture = Rs. $(\frac{100}{110} \times 68.20)$ = Rs. 62 By the rule of alligation, we have: ∴ Required ratio = 3 : 2

29.

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

30.

40 litres of a mixture of milk and water contains 10% of water, the water to be added, to make the water content 20% in the new mixture. Find how many litres water will be added ?

(A) 6 litres
(B) 6.5 litres
(C) 5.5 litres
(D) 5 litres

Solution: Water content in 40 litres of mixture. $\begin{aligned} = 40 \times \frac{10}{100} \\ = 4 litres \end{aligned}$ ∴ Milk in the mixture. $\begin{aligned} = 40 - 4 \\ = 36 litres \end{aligned}$ Let x litres of water is mixed $\begin{aligned} \Rightarrow \frac{4 + x}{40 + x} = \frac{20}{100} \\ \Rightarrow x = 5 litres \end{aligned}$

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Practice MCQ Questions and Answer on Alligation

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