Quantitative Aptitude

Mixtures and Alligation

1,816 Questions
All Direct removal and addition 448 Alligation cross rule 270 Ratios, quantities, and percentages 233 Weighted mean and concentration 195 Equal quantity replacement 189 Three or more components 174 Repeated equal-volume replacement 154 Profit-based alligation 153

Mixtures and Alligation Questions

Multiple choice

A dairyman pays Rs. 6.4 per litre for milk. He adds water and sells the mixture at Rs. 8 per litre, thereby making 37.5% profit. The ratio of water to milk received by the customer is

  1. 1 : 15

  2. 1 : 10

  3. 1 : 20

  4. 1 : 12

  5. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the cost price of milk be 6.4 and the selling price be 8. The profit is 37.5%, meaning the cost price of the mixture is 8 / 1.375 = 5.818. Using the alligation rule: (Milk cost - Mixture cost) / (Mixture cost - Water cost) = (6.4 - 5.818) / (5.818 - 0) = 0.582 / 5.818, which simplifies to 1/10.

Multiple choice

Three identical beakers are fully-filled to capacity with mixtures of wheat and rice. The ratio of wheat to rice in the first beaker is 3 : 4, that in the second beaker is 4 : 5 and that in the third beaker is 5 : 6. The contents of the three breakers are emptied into a single vessel. What is the ratio of wheat to rice in the mixture now?

  1. 11 : 9

  2. 143 : 60

  3. 920 : 1159

  4. 1159 : 920

  5. 9 : 11
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Beakers are identical, so assume each has 1 unit volume. Wheat in beakers: 3/7, 4/9, 5/11. Rice: 4/7, 5/9, 6/11. Total wheat = 3/7 + 4/9 + 5/11 = (297 + 308 + 315) / 693 = 920/693. Total rice = 4/7 + 5/9 + 6/11 = (396 + 385 + 378) / 693 = 1159/693. Ratio = 920 : 1159.

Multiple choice

An alloy contains zinc and tin in the ratio 3 : 4. Another alloy contains zinc and silver in the ratio 4 : 3. If both the alloys are melted and mixed in equal ratio, what will be the ratio of zinc and tin in the new alloy?

  1. 4 : 3

  2. 7 : 4

  3. 1 : 1

  4. 3 : 1
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Alloy 1 has Zinc:Tin = 3:4. Alloy 2 has Zinc:Silver = 4:3. Mixing equal parts means taking 1/2 of each. Zinc content = 1/2(3/7) + 1/2(4/7) = 7/14 = 1/2. Tin content = 1/2(4/7) = 2/7. The ratio of Zinc to Tin is (1/2) / (2/7) = 7/4.

Multiple choice

One vessel contains water and another vessel contains spirit. Half of the water is poured into the spirit and an equal quantity of the mixture is poured back into the water. If the first vessel contained water and spirit in the ratio of 9 : 4, compare the ratio of initial quantities of water and spirit in two vessel.

  1. 1 : 2

  2. 3 : 4

  3. 2 : 3

  4. 5 : 4

  5. 4 : 5
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The problem describes a process of swapping mixtures between two vessels. Given the ratio 9:4 in the first vessel and the nature of the exchange, the initial quantities must satisfy the conservation of the total volume and the specific ratio provided. Solving the balance equations leads to the ratio 5:4.

Multiple choice

If 20 litres of solution containing 15% alcohol is mixed with 30 litres of solution containing 18% alcohol, find the concentration of alcohol in the resulting solution.

  1. 15 4 5 %

  2. 16 4 5 %

  3. 17 4 5 %

  4. 18 4 5 %

  5. 14 1 5 %
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The first solution contains 20 x 15/100 = 3 litres of alcohol, and the second contains 30 x 18/100 = 5.4 litres. The mixture therefore has 8.4 litres of alcohol in 50 litres, giving 8.4/50 x 100 = 16.8%, or 16 4/5%.

Multiple choice

Two vessels A and B contain mixtures of acid and water in the ratios of 4 : 3 and 5 : 3 respectively. Find the ratio in which these mixtures should be mixed to obtain a new mixture in vessel C containing acid and water in the ratio of 3 : 2.

  1. 5 : 8

  2. 7 : 8

  3. 7 : 5

  4. 4 : 7
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the allegation method on the acid content: Vessel A has 4/7, Vessel B has 5/8, and the mixture has 3/5. The differences are |5/8 - 3/5| = 1/40 and |4/7 - 3/5| = 1/35. The ratio is (1/40) : (1/35) = 35 : 40 = 7 : 8.