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 manufacturer has 600 litres of a 12% solution of acid. How many litres (x) of a 30% acid solution must be added to it so that acid content in the resulting mixture will be more than 15% but less than 18%?

  1. 120 < x < 300

  2. 100 < x < 270

  3. 150 < x < 320

  4. 180 < x < 370
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial: 600L at 12% = 72L acid. Added: xL at 30% = 0.3xL acid. Total: (72 + 0.3x) / (600 + x). We need 0.15 < (72 + 0.3x)/(600 + x) < 0.18. Solving 0.15(600+x) < 72+0.3x gives 90 + 0.15x < 72 + 0.3x -> 18 < 0.15x -> x > 120. Solving (72+0.3x) < 0.18(600+x) gives 72 + 0.3x < 108 + 0.18x -> 0.12x < 36 -> x < 300.

Multiple choice

A black jute bag contains 'L' kg of red lentils. In order to make a mixture of pulses, he takes out 30 kg of red lentils from the black bag and adds 20 kg of Bengal grams in the black bag after which the ratio of Red lentils to Bengal grams in the bag becomes 3 : 2. If another white jute bag contains Red lentils 'G' kg more than that in the black bag initially and if 25 kg of Bengal grams is added, then the ratio of Red lentils to Bengal grams becomes 4 : 1. Find the value of G.

  1. 45

  2. 50

  3. 40

  4. 30

  5. 35
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Black bag: (L-30)/20 = 3/2 => 2L-60 = 60 => L=60. White bag: (L+G)/25 = 4/1 => 60+G = 100 => G=40.

Multiple choice

A measuring cup contains 1/5 of a cup of orange juice. It is then filled to the 1 cup mark with a mixture that contains equal amounts of orange, grapefruit, and pineapple juices. What fraction of the final mixture is orange juice?

  1. 1/15

  2. 4/15

  3. 7/15

  4. 11/15
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial juice = 1/5 cup. Added mixture = 4/5 cup. The mixture contains equal parts of 3 juices, so orange juice in the added part = 1/3 * 4/5 = 4/15. Total orange juice = 1/5 + 4/15 = 3/15 + 4/15 = 7/15.

Multiple choice

In a mixture of juice, 22% is water and the remaining is juice. After removing and replacing 8 litres of the mixture with 8 litres of pure juice, the percentage of juice in the mixture increases to 81%. What was the original quantity of the mixture?

  1. 63 litres

  2. 91.67 litres

  3. 117 litres

  4. 58.67 litres

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

Let initial mixture be X. Juice is 78% of X. Removing 8L removes 0.78*8 = 6.24L of juice. Adding 8L of pure juice adds 8L. New juice amount = 0.78X - 6.24 + 8 = 0.78X + 1.76. New concentration = (0.78X + 1.76)/X = 0.81. 0.78X + 1.76 = 0.81X, so 0.03X = 1.76, X = 58.67.

Multiple choice

A chemist has two solutions: one is a 20% saline solution, and the other is a 30% saline solution. He wants to mix these two solutions to create a new solution of 250 mL, such that the resulting mixture has the maximum possible percentage of saline. However, the chemist is allowed to use at least 100 mL of the 20% solution. What is the maximum percentage of saline that can be achieved in the final mixture?

  1. 22%

  2. 24%

  3. 26%

  4. 28%

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

To maximize saline concentration, use as much of the 30% solution as possible. We need 250 mL total and at least 100 mL of 20% solution. Using exactly 100 mL of 20% and 150 mL of 30% gives (100*0.2 + 150*0.3)/250 = (20+45)/250 = 65/250 = 0.26 = 26%.

Multiple choice

The owner of a grocery shop purchases two varieties of grain. The price of the first variety is twice the price of the second one. He mixes both the varieties and sells the mixture at a price of Rs. 28 per kg, making a profit of 25%. If the ratio of the first variety of grain and the second variety of grain in the mixture is 2 : 3, find the price of the first variety of grain.

  1. Rs. 16/kg

  2. Rs. 24/kg

  3. Rs. 32/kg

  4. Rs. 64/kg
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let prices be 2x and x. Ratio 2:3. Average cost = (2*2x + 3*x) / 5 = 7x/5. Selling price = 28, profit 25%. Cost price = 28 / 1.25 = 22.4. 7x/5 = 22.4 => 7x = 112 => x = 16. Price of first variety = 2x = 32.

Multiple choice

Anita created a batch of green paint by mixing 2 ounces of blue paint with 3 ounces of yellow paint. She must mix a second batch using the same ratio of blue and yellow paint as the first batch. If she uses 5 ounces of blue paint for the second batch, how much yellow paint should Anita use?

  1. Exactly 5 ounces

  2. 3 ounces more than the amount of yellow paint used in the first batch

  3. 2.5 times the amount of yellow paint used in the first batch

  4. 2.5 times the amount of blue paint used in the second batch
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Ratio of blue to yellow is 2:3. For 5 ounces of blue, the amount of yellow is (3/2) * 5 = 7.5 ounces. Comparing 7.5 to the original 3 ounces: 7.5 = 2.5 * 3.

Multiple choice

A person buys tea of three different qualities at Rs. 800, Rs. 500, and Rs. 300 per kg, respectively, and the amounts bought are in the proportion 2 : 3 : 5. She mixes all the tea and sells one-sixth of the mixture at Rs. 700 per kg. The price, in INR per kg, at which she should sell the remaining tea, to make an overall profit of 50%, is

  1. 653

  2. 688

  3. 692

  4. 675
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let amounts be 2k, 3k, 5k. Total mass = 10k. Cost = 2k*800 + 3k*500 + 5k*300 = 1600k + 1500k + 1500k = 4600k. Target Revenue = 4600k * 1.5 = 6900k. Sold 1/6 of 10k = 5k/3 at 700 = 3500k/3. Remaining 25k/3 must be sold for 6900k - 3500k/3 = 17200k/3. Price = (17200k/3) / (25k/3) = 17200/25 = 688.

Multiple choice

Two alcohol solutions, A and B, are mixed in the proportion of 1 : 3 by volume. The volume of the mixture is then doubled by adding solution A such that the resulting mixture has 72% alcohol. If solution A has 60% alcohol, then the percentage of alcohol in solution B is ____. (Key in the integer)

  1. 94%

  2. 92%

  3. 90%

  4. 89%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let solution A have volume V and solution B have 3V. Total volume = 4V. Adding A to double the volume means adding 4V of A. Total volume = 8V. Total alcohol = (V * 0.60) + (3V * x) + (4V * 0.60) = 8V * 0.72. 0.6 + 3x + 2.4 = 5.76. 3x = 2.76. x = 0.92 or 92%.

Multiple choice

A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio 1 : 3, then the ratio of lemon juice and sugar syrup in the new mixture is

  1. 1 : 6

  2. 1 : 4

  3. 1 : 5

  4. 1 : 7
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Mixture 1: 1 part lemon, 1 part sugar (ratio 1:1). Mixture 2: 1 part Mixture 1, 3 parts sugar. Total lemon = 1/2 part. Total sugar = 1/2 (from Mix 1) + 3 = 3.5 parts. Ratio = 0.5 : 3.5 = 1 : 7.

Multiple choice

There are two containers of the same volume, first container half-filled with sugar syrup and the second container half-filled with milk. Half the content of the first container is transferred to the second container, and then the half of this mixture is transferred back to the first container. Next, half the content of the first container is transferred back to the second container. Then the ratio of sugar syrup and milk in the second container is

  1. 5 : 6

  2. 5 : 4

  3. 6 : 5

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