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

Milk and water are mixed in the ratio 4 : 1 to form solution A and in the ratio 3 : 2 to form solution B. A man takes equal quantities of solutions A and B and mixes them together. What is the ratio of quantities of milk to that of water in the mixture so formed?

  1. 7 : 3

  2. 1 : 1

  3. 3 : 7

  4. 3 : 2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Solution A has milk:water = 4:1 (4/5 milk, 1/5 water). Solution B has milk:water = 3:2 (3/5 milk, 2/5 water). Mixing equal quantities means taking 1/2 of each. Total milk = 1/2 * (4/5 + 3/5) = 7/10. Total water = 1/2 * (1/5 + 2/5) = 3/10. The ratio is 7:3.

Multiple choice

Mixture of milk and water has been kept in two separate containers. Ratio of milk to water in one of the containers is 5 : 1 and that in the other container is 7 : 2. In what ratio should the mixtures of these two containers be added together so that the quantity of milk in the new mixture may become 80%?

  1. 3 : 2

  2. 2 : 3

  3. 4 : 5

  4. None of these

  5. 3 : 5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Milk fractions: 5/6 and 7/9. Target: 4/5. Using alligation: |7/9 - 4/5| : |4/5 - 5/6| = |35-36/45| : |24-25/30| = 1/45 : 1/30 = 30:45 = 2:3.

Multiple choice

There are two taps P and Q. Milk flows out from tap P, whereas water flows out from tap Q. P alone can fill the tank in 20 hours and Q alone can fill the tank in 60 hours. When the tank is empty, tap P is opened. After how much time should tap Q be opened so that the ratio of milk and water in the tank is 5 : 1, when the tank is full?

  1. 4 hours

  2. 5 hours

  3. 6.66 hours

  4. 8.33 hours

  5. 10 hours
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let P be open for T hours and Q be open for (T-x) hours. P fills 1/20 per hour, Q fills 1/60 per hour. Total volume = T/20 + (T-x)/60 = 1. Ratio of milk to water = (T/20) / ((T-x)/60) = 5/1. 3T / (T-x) = 5 => 3T = 5T - 5x => 2T = 5x => x = 0.4T. Substituting into T/20 + (T-0.4T)/60 = 1 => 3T + 0.6T = 60 => 3.6T = 60 => T = 16.66. x = 0.4 * 16.66 = 6.66.

Multiple choice

For making a colour A, three liquids x, y and z are mixed in the ratio 3 : 5 : 7. For colour B, the ratio is 1 : 8 : 3. If 10 parts of colour A are mixed with 8 parts of colour B, what is the ratio of liquids x, y and z in the resulting mixture?

  1. 11 : 25 : 17

  2. 31 : 27 : 30

  3. 18 : 25 : 19

  4. 4 : 13 : 10

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A: x=3/15, y=5/15, z=7/15. B: x=1/12, y=8/12, z=3/12. 10 parts A + 8 parts B: x = 10*(3/15) + 8*(1/12) = 2 + 2/3 = 8/3. y = 10*(5/15) + 8*(8/12) = 10/3 + 16/3 = 26/3. z = 10*(7/15) + 8*(3/12) = 14/3 + 2 = 20/3. Ratio = 8:26:20 = 4:13:10.

Multiple choice

Raman has a mixture of milk and water in the ratio 5 : 4. If 16 litres of water is added to the mixture, the ratio turns into 5 : 6. Find out the total quantity of milk in the given mixture.

  1. 38 litres

  2. 40 litres

  3. 480 litres

  4. 384 litres

  5. 500 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the initial quantities be 5x and 4x. Adding 16 liters of water changes the ratio to 5x / (4x + 16) = 5/6. Solving this gives 30x = 20x + 80, so 10x = 80 and x = 8. The milk quantity is 5 * 8 = 40 litres.

Multiple choice

Shweta purchased a variety of rice at Rs. 65 per kg and mixed it with 5 kg of another variety of rice that she had purchased at Rs. 58 per kg. If she gains 10% on selling the mixture at Rs. 66 per kg, then what was the quantity of rice that she had purchased at Rs. 65 per kg?

  1. 1 kg

  2. 2 kg

  3. 3 kg

  4. 5 kg

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

Let x be the quantity of rice at 65 Rs/kg. Total cost = 65x + 5*58. Selling price = 66(x+5). Profit is 10%, so 1.1 * (65x + 290) = 66(x+5). Solving for x gives 71.5x + 319 = 66x + 330, so 5.5x = 11, x = 2.

Multiple choice

Vessels A and B contain milk and water mixed in the ratio 5 : 2 and 7 : 6, respectively. In what ratio must these mixtures be mixed to form a new mixture in vessel C containing milk and water in the ratio 8 : 5?

  1. 6 : 9

  2. 7 : 9

  3. 8 : 9

  4. 9 : 10

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

Using the method of alligation, the fraction of milk in vessel A is 5/7, in vessel B is 7/13, and in the mixture is 8/13. The difference between A and the mixture is |5/7 - 8/13| = |65-56|/91 = 9/91, and between B and the mixture is |7/13 - 8/13| = 1/13 = 7/91. The ratio is 7/91 : 9/91 = 7 : 9.

Multiple choice

A vessel contains a mixture of 30 L petrol, 15 L diesel and 8 L kerosene. Y L petrol, Y L diesel and Y L kerosene are taken away from the mixture. If 20% of the new mixture is 7 L, then, find the ratio of petrol, diesel and kerosene in new mixture.

  1. 24 : 9 : 2

  2. 12 : 5 : 1

  3. 27 : 12 : 5

  4. 36 : 21 : 14

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial mixture: 30P, 15D, 8K (Total 53). After removing Y of each, remaining is (30-Y)P, (15-Y)D, (8-Y)K. Total remaining = 53 - 3Y. 20% of (53-3Y) = 7 implies 53-3Y = 35, so 3Y = 18, Y = 6. New mixture: 24P, 9D, 2K. Ratio is 24:9:2.