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 shopkeeper bought three varieties of apples: one costing Rs. 147 per kg, second costing Rs. 150 per kg and third costing Rs. 153 per kg and he mixed these apples in the ratio (in term of weight) 17 : 19 : 21 respectively. If he sold all the apples at Rs. 151 per kg, then what is his overall profit/ loss?

  1. 0.45% profit

  2. 0.45% loss

  3. 0.525% profit

  4. No profit, no loss

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

Weighted average cost price = (147*17 + 150*19 + 153*21) / (17+19+21) = (2499 + 2850 + 3213) / 57 = 8562 / 57 = 150.21 approx. Selling price is 151. Profit = 151 - 150.21 = 0.79. Profit percentage = (0.79 / 150.21) * 100 which is approximately 0.525%.

Multiple choice

Ashok purchased two qualities of grains at the rate of Rs 100 per quintal and Rs 160 per quintal. In 50 quintals of the second quality, how much grain of the first quality should be mixed so that by selling the resulting mixture at Rs 195 per quintal, he gains a profit of 30%?

  1. 10 quintals

  2. 14 quintals

  3. 20 quintals

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

Selling price = 195. Profit = 30%, so cost price = 195 / 1.3 = 150. Using the mixture rule: (160-150) / (150-100) = 10/50 = 1/5. So 1 part of 100-grain for 5 parts of 160-grain. 50/5 = 10 quintals.

Multiple choice

How many kilograms of salt worth Rs 360 per kg should be mixed with 10 kg of salt worth Rs420 per kg, such that by selling the mixture at Rs 480 per kg, there may be a gain of 20%?

  1. 5 kg

  2. 3 kg

  3. 2 kg

  4. 4 kg
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Selling price = 480, gain = 20%. Cost price of mixture = 480 / 1.2 = 400 per kg. Using alligation: (420-400) / (400-360) = 20 / 40 = 1/2. Ratio of 360-salt to 420-salt is 1:2. Since we have 10 kg of 420-salt, we need 5 kg of 360-salt.

Multiple choice

A 10 percent gain is made by selling the mixture of two types of milk at Rs 48 per kg. If the type costing Rs 61 per kg was mixed with 100 kg of the other, how many kilograms of the former was mixed?

  1. 38 kg

  2. 30.5 kg

  3. 19 kg

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Selling price = 48, gain = 10%, so Cost Price = 48 / 1.1 = 43.63. We have two types of milk: 61/kg and an unknown cost for the 100kg. Without the cost of the second type, the mixture ratio cannot be determined.

Multiple choice

From a full barrel containing 729 litres of honey we pour off 'a' litre and add water to fill up the barrel. After stirring the solution thoroughly, we pour off 'a' litre of the solution and again add water to fill up the barrel. After the procedure is repeated 6 times, the solution in the barrel contains 64 litres of honey. Find a.

  1. 243 litres

  2. 81 litres

  3. 2.7 litres

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

The formula for remaining honey is Initial * (1 - a/V)^n = Final. 729 * (1 - a/729)^6 = 64. (1 - a/729)^6 = 64/729 = (2/3)^6. So 1 - a/729 = 2/3, which means a/729 = 1/3, so a = 243.

Multiple choice

In what proportion must water be mixed with honey so as to gain 10% by selling the mixture at the cost price of the honey? (Assume that water is freely available)

  1. 1 : 4

  2. 1 : 5

  3. 1 : 6

  4. 1 : 10
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let CP of honey be 1 per unit. To gain 10%, SP must be 1.1. Since water is free, the cost is only the honey. If we sell (1+x) units of mixture for 1.1, where 1 unit is honey and x is water, the cost is 1. So 1.1 = 1 + profit. This is not quite right. Let CP = 1. To gain 10%, we need to sell 1 unit of honey for 1.1. If we mix water, the volume becomes 1+x. Selling at cost price of honey means selling 1+x units for 1+x. If we want 10% profit, 1.1 * (Cost of 1 unit) = 1 * (Price of 1 unit). The ratio of water to honey is 1:10.

Multiple choice

Two types of tea are mixed in the ratio of 3 : 5 to produce the first quality and if they are mixed in the ratio of 2 : 3, the second quality is obtained. How many kilograms of the first quality has to be mixed with 10 kg of the second quality so that a third quality having the two varieties in the ratio of 7 : 11 may be produced?

  1. 5 kg

  2. 10 kg

  3. 8 kg

  4. 9 kg
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x be the amount of first quality tea. The first quality has ratio 3:5 (total 8 parts), second has 2:3 (total 5 parts). The third quality has 7:11 (total 18 parts). This is a mixture problem requiring setting up equations based on the proportions of the two varieties.

Multiple choice

Two vessels A and B of equal volume contain milk and water in the ratio 3 : 2 and 2 : 1 to their brim respectively. Two litres of the solution from vessel A and three litres of the solution from vessel B are poured into a big empty vessel C. If the solution in C occupied 40% of the capacity of C, what proportion of the volume of vessel C should be the volume of water that shall be added so that the ratio of milk and water in vessel C becomes 1 : 1?

  1. 21/125

  2. 2/25

  3. 4/75

  4. 14/125

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

Vessel A: 2L, 3:2 ratio (1.2L milk, 0.8L water). Vessel B: 3L, 2:1 ratio (2L milk, 1L water). Total in C: 3.2L milk, 1.8L water (Total 5L). C is 40% full, so capacity = 5/0.4 = 12.5L. To get 1:1 ratio, we need 3.2L water total. Currently 1.8L, so add 1.4L water. 1.4/12.5 = 14/125.