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

Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution R in the liquid in the tank after 3 minutes?

  1. 8/11

  2. 7/11

  3. 6/11

  4. 5/11
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Rates: A=1/30, B=1/20, C=1/10. In 3 minutes: A fills 3/30=1/10, B fills 3/20, C fills 3/10. Total filled = 1/10 + 3/20 + 3/10 = 2/20 + 3/20 + 6/20 = 11/20. The proportion of R (from C) is (3/10) / (11/20) = (6/20) / (11/20) = 6/11.

Multiple choice

In three containers of Alcohol 10L capacity, mixture of alcohol and water is filled. The ratio of alcohol and water are 2 : 1, 3 : 1 and 3 : 2 in the respective vessels. If all the three vessels are emptied into a single large vessel, find the ratio of alcohol and water in the resultant mixture.

  1. 121:63

  2. 122:59

  3. 121:59

  4. 121:95
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total alcohol = 10*(2/3) + 10*(3/4) + 10*(3/5) = 20/3 + 30/4 + 30/5 = 6.66 + 7.5 + 6 = 20.16. Total water = 10*(1/3) + 10*(1/4) + 10*(2/5) = 3.33 + 2.5 + 4 = 9.83. Ratio = 20.16 / 9.83. Using fractions: (400+450+360)/60 : (200+150+240)/60 = 1210/60 : 590/60 = 121:59.

Multiple choice

A barrel contains 60 litres of alcohol and water. The quantity of alcohol is 12 litres more than water. Some amount of water is added to this barrel such that the ratio of alcohol to water becomes 18 : 17. How much water is added to barrel?

  1. 12 litres

  2. 13 litres

  3. 10 litres

  4. 8 litres

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

Initial: A+W=60, A-W=12. Solving gives A=36, W=24. Let x be water added: 36 / (24+x) = 18/17. 36*17 = 18(24+x). 2*17 = 24+x. 34 = 24+x, so x=10.

Multiple choice

A vessel contains 120 litres of milk. 24 litres of milk is taken out from it and replaced by water. Then again from mixture, 24 litres is taken out and replaced by water. The ratio of milk and water in the resultant mixture is- একটি পাত্রে 120 লিটার দুধ আছে। এখান থেকে 24 লিটার দুধ জল দ্বারা প্রতিস্থাপন করা হল। পুনরায় 24 লিটার দুধ জল দ্বারা প্রতিস্থাপন করা হলো। এখন পাত্রটিতে দুধ এবং জলের অনুপাত কত হবে?

  1. 4 : 3

  2. 16 : 9

  3. 3 : 4

  4. 8 : 13
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial milk = 120. After 1st replacement: Milk = 120 * (1 - 24/120) = 120 * 0.8 = 96. After 2nd replacement: Milk = 96 * 0.8 = 76.8. Water = 120 - 76.8 = 43.2. Ratio = 76.8 : 43.2 = 768 : 432 = 16 : 9.

Multiple choice

A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second can contains 50% water. How much of the mixture should he mix from each of the containers, so as to get 12 litres of solution such that the ratio of water to pure milk is 3 : 5?

  1. 4 litres, 8 litres

  2. 6 litres, 6 litres

  3. 5 litres, 7 litres

  4. 7 litres, 5 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Can 1: 25% water (1/4). Can 2: 50% water (1/2). Target: 12L with 3:5 water to milk ratio, which is 3/8 water (37.5%). Using alligation: (1/2 - 3/8) : (3/8 - 1/4) = (1/8) : (1/8) = 1:1. Total 12L means 6L from each.

Multiple choice

In what ratio should water be added to soda costing Rs. 12 per litre so as to make a profit of 25% by selling the diluted liquid at Rs. 13.75 per litre?

  1. 5 : 7

  2. 1 : 11

  3. 7 : 2

  4. 2 : 7
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the ratio of water to soda be x:1. Cost of soda = 12. Cost of water = 0. Total cost = 12. Selling price = 13.75. Profit = 25%, so Cost * 1.25 = 13.75. Cost = 13.75 / 1.25 = 11. Using the mixture rule: (12*1 + 0*x) / (1+x) = 11. 12 = 11 + 11x, so 11x = 1, x = 1/11.

Multiple choice

A solution contains some alcohol and some water in ratio 3 : 2. If another 200 ml of solution with equal proportion of alcohol and water is added to the given solution, ratio of alcohol to water becomes 4 : 3. What was the amount of water in initially given solution?

  1. 100 ml

  2. 150 ml

  3. 200 ml

  4. 300 ml

  5. 500 ml
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let initial alcohol be 3x and water be 2x. Total = 5x. Adding 200 ml of 1:1 solution means adding 100 ml alcohol and 100 ml water. New ratio: (3x + 100) / (2x + 100) = 4/3. 9x + 300 = 8x + 400 => x = 100. Initial water = 2x = 200 ml.

Multiple choice

48 litre of Glycerin is mixed with 144 litre Rose water. D litre of total mixture is taken out and 32 litre Glycerin and 48 litre Rose water are added in the mixture. The final mixture contains 30% Glycerin, find the quantity of the mixture that is taken out.

  1. 24 litres

  2. 32 litres

  3. 40 litres

  4. 20 litres

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

Initial: 48G, 144R (Total 192). Remove D: (48-D/4)G, (144-3D/4)R. Add 32G, 48R: (80-D/4)G, (192-3D/4)R. Total mixture = 192-D+80 = 272-D. Glycerin % = (80-D/4)/(272-D) = 0.3. 80-0.25D = 81.6 - 0.3D. 0.05D = 1.6. D = 32.