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

Q. 10. A cask contains a mixture of two liquids P and Q in the ratio 7 : 5. When 6 L of this mixture is taken out from the cask and an equal volume is filled with Q, the ratio of P and Q becomes 21 : 19. Find the initial volume of the mixture in the cask.

  1. 30L

  2. 45L

  3. 60L

  4. 42L
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let initial volume be V. Liquid P = 7/12 V, Q = 5/12 V. Removing 6L removes 3.5L of P and 2.5L of Q. Remaining: P = 7/12 V - 3.5, Q = 5/12 V - 2.5. Adding 6L of Q: P = 7/12 V - 3.5, Q = 5/12 V + 3.5. Ratio (7/12 V - 3.5) / (5/12 V + 3.5) = 21/19. Solving for V gives 60L.

Multiple choice

The concentration of milk in a 60L milk and water solution is 30%. If 6L of the solution is replaced by water and then 5L of the resulting solution is again replaced by water, then find the concentration of milk in the final solution.

  1. 24.50%

  2. 25.00%

  3. 24.75%

  4. 25.50%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial milk = 0.3 * 60 = 18L. After replacing 6L of solution (10% of total), milk remaining = 18 * 0.9 = 16.2L. After replacing 5L of the new 60L solution (5/60 = 1/12), milk remaining = 16.2 * (1 - 1/12) = 16.2 * (11/12) = 14.85L. Concentration = 14.85 / 60 = 0.2475 = 24.75%.

Multiple choice

A painter has a 1-liter paint can of pure blue paint. To achieve different shades, he mix it with white paint following a specific mixing guide. The painter removes two-thirds of the mixture from the can and replaces it with white paint. This mixing step is repeated three times. What is the final ratio of blue paint to white paint in the can after the third mixing?

  1. 2 : 13

  2. 1 : 13

  3. 1 : 8

  4. 1 : 26

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

After removing 2/3, 1/3 of the blue paint remains. This is repeated 3 times: (1/3)^3 = 1/27 of blue paint remains. The rest is white paint (26/27). Ratio of blue to white is 1/27 : 26/27 = 1:26.

Multiple choice

Amount of mixture of milk and water in container A is Ratio of milk and water is 7 : 5. Another vessel contains 50 L of pure milk. 40% mixture from container A taken out and mixed in Manother vessel and now ratio of milk and water in another vessel is 39 : 10. Find which of the following values satisfy the blank.

  1. 144

  2. 120

  3. 156

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

If the initial amount is x litres, the removed mixture contains 7x/30 litres of milk and x/6 litres of water. After adding it to 50 litres of milk, the ratio equation gives (50 + 7x/30):(x/6) = 39:10, resulting in x = 120 litres.

Multiple choice

A bucket is filled with syrup. Half of its content is poured out and replaced with water. If this process of pouring out half of the content and replacing it with water is repeated five more times, then the final ratio of syrup to water in the bucket is

  1. 1 : 31

  2. 1 : 63

  3. 1 : 32

  4. 1 : 64

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

Initial syrup = 1. After 6 operations of replacing half: Syrup remaining = 1 * (1/2)^6 = 1/64. Water = 1 - 1/64 = 63/64. Ratio = 1/64 : 63/64 = 1 : 63.

Multiple choice

A tank held a certain amount of a solution of sugar and water. After adding 20 litres of water, the concentration of sugar in the new solution became 50%. Subsequently, 60 kg of sugar is dissolved into this new solution, the final concentration of sugar rose to 75%. The ratio of water and sugar in the original solution was:

  1. 1 : 3

  2. 3 : 2

  3. 5 : 3

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

Let original water be W and sugar be S. After adding 20L water, concentration is 50%, so S / (W + 20 + S) = 0.5 => S = W + 20. Adding 60kg sugar, concentration is 75%, so (S + 60) / (W + 20 + S + 60) = 0.75. Substituting S = W + 20: (W + 80) / (2W + 100) = 0.75 => W + 80 = 1.5W + 75 => 0.5W = 5 => W = 10. Then S = 30. Ratio W:S = 10:30 = 1:3.

Multiple choice

From a sample containing 200 ml of sodium hydroxide, 20 ml was taken out and was replaced with water. Again, 40 ml of mixture was taken out and replaced with water. Finally, 50 ml of mixture was taken out and replaced with water. Find the quantity of water in the final mixture.

  1. 72 ml

  2. 86 ml

  3. 92 ml

  4. 108 ml

  5. 120 ml
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial NaOH = 200. After 20ml out/water in: NaOH = 200 * (180/200) = 180. After 40ml out/water in: NaOH = 180 * (160/200) = 144. After 50ml out/water in: NaOH = 144 * (150/200) = 108. Water = 200 - 108 = 92 ml.

Multiple choice

Two mixtures A and B are in the ratio 5 : 4, respectively. Mixture A contains p% of paint and q% of thinner, and mixture B contains r% of paint and s% of thinner. If mixture A is mixed with mixture B, the final quantity of paint becomes 30% of the total volume of final mixture. If p - r = 27, find p : r.

  1. 5 : 14

  2. 14 : 5

  3. 15 : 4

  4. 4 : 15

  5. 16 : 5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let volumes be 5x and 4x. Total volume = 9x. Paint = (p/100)*5x + (r/100)*4x = 0.30 * 9x. 5p + 4r = 270. Given p - r = 27 => p = r + 27. Substitute: 5(r+27) + 4r = 270 => 9r + 135 = 270 => 9r = 135 => r = 15. Then p = 42. p:r = 42:15 = 14:5.

Multiple choice

In a steel factory, an engineer prepared two alloys L and M of iron and carbon by mixing the metals in the ratios 8 : 3 and 8 : 13, respectively. If equal quantities of the alloys are melted to form a third alloy O, then what is the ratio of iron and carbon in alloy O?

  1. 128 : 103

  2. 51 : 43

  3. 49 : 13

  4. 19 : 21

  5. 15 : 28
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Alloy L has iron and carbon in ratio 8:3 (total 11 parts), so iron is 8/11 and carbon is 3/11. Alloy M has ratio 8:13 (total 21 parts), so iron is 8/21 and carbon is 13/21. Mixing equal quantities means taking the average of the fractions: Iron = (8/11 + 8/21)/2 = (168+88)/(231*2) = 256/462 = 128/231. Carbon = (3/11 + 13/21)/2 = (63+143)/(231*2) = 206/462 = 103/231. The ratio is 128:103.

Multiple choice

A beaker had citric acid and some water mixed in it in the ratio of 4 : 1. 10 ml of the solution is taken out 10 ml of water is poured into it. The present ratio of the citric acid and water is 2 : 3. How much citric acid was present in the glass in the beginning?

  1. 4 ml

  2. 8 ml

  3. 16 ml

  4. 40 ml

  5. 42 ml
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let initial acid be 4x and water be x. Total = 5x. After removing 10ml, acid = 4x - 8, water = x - 2. Adding 10ml water: acid = 4x - 8, water = x + 8. Ratio (4x-8)/(x+8) = 2/3. 12x - 24 = 2x + 16, 10x = 40, x = 4. Initial acid = 4*4 = 16 ml.