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 jar is filled with a mixture of two liquids $A$ and $B$ in the proportion $A:B:: 5:3,$ when $16$ litres of the mixture is drawn off and the jar is filled with liquid $B,$ then the proportion becomes $A:B::3:5.$ How many litres of mixture does the jar hold?
  1. $35$ $L$
  2. $50$ $L$
  3. $45$ $L$
  4. $40$ $L$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the jar hold 8x total. A = 5x, B = 3x. Removing 16L removes 10L of A and 6L of B. Remaining: A = 5x - 10, B = 3x - 6 + 16 = 3x + 10. Ratio (5x-10)/(3x+10) = 3/5. 25x - 50 = 9x + 30, 16x = 80, x = 5. Total = 8x = 40L.

Multiple choice

There are three containers of equal capacity The ratio of sulphuric acid to water in the first container is 3 : 2 that in the second container is 7 : 3 and in the third container it is 11 : 4 If all the liquids are mixed together then the ratio of sulphuric acid to water in the mixture will be

  1. 61 : 29

  2. 61 : 28

  3. 60 : 29

  4. 59 : 29
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total acid = 3/5 + 7/10 + 11/15 = (18 + 21 + 22) / 30 = 61/30. Total water = 2/5 + 3/10 + 4/15 = (12 + 9 + 8) / 30 = 29/30. The ratio is 61:29.

Multiple choice

Two vessels $A$ and $B$ contain milk and water in the ratio of $5 : 2$ and $2 : 3$. When these mixtures are mixed to form a new mixture containing half milk and half water, they must be taken in the ratio :
  1. $2 : 5$
  2. $7 : 3$
  3. $1 : 2$
  4. $4 : 5$
  5. $7 : 15$

  6. None of these 
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Use the rule of alligation. Vessel A: milk fraction 5/7. Vessel B: milk fraction 2/5. Target mixture: 1/2. Differences: |5/7 - 1/2| = 3/14 and |2/5 - 1/2| = 1/10. The ratio is (1/10) : (3/14) = 14 : 30 = 7 : 15.

Multiple choice

A bottle is 80% full. The liquid in the bottle consists of 60% guava juice and 40% pineapple juice. The remainder of the bottle is then filled with 200 mL of rum. How much guava juice is in the bottle ?
  1. $350$ mL
  2. $480$ mL
  3. $500$ mL
  4. $460$ mL
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial volume = 80% of bottle. Let total capacity be V. Initial liquid = 0.8V. Guava = 0.6 * 0.8V = 0.48V. Adding 200mL makes it full, so 0.2V = 200, V = 1000mL. Guava = 0.48 * 1000 = 480mL.

Multiple choice

A milk can contain $112$ litre of milk. How many liters of milk should be removed and same amount if water if added, the proportion of milk to water comes to be $13:3 ?$
  1. $\dfrac{336}{16}$
  2. $\dfrac{158}{13}$
  3. $\dfrac{178}{16}$
  4. $\dfrac{138}{13}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let x be the amount removed. The final milk amount is 112 - x + (x * 0) = 112 - x. The final water amount is x. The ratio (112-x)/x = 13/3. 336 - 3x = 13x, so 16x = 336, x = 336/16 = 21.

Multiple choice

Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are $ 5 : 3$ and $1 : 2$ respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio of $4 : 3.$ What is the ratio of the composition of the basic elements in alloy X?
  1.  $1 : 1$
  2. $2 : 3$
  3. $5 : 2$
  4. $4 : 3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Alloy A: 5/8 and 3/8. Alloy B: 1/3 and 2/3. Mixing 4 parts A and 3 parts B: Total parts = 7. Element 1 = (4 * 5/8 + 3 * 1/3) / 7 = (2.5 + 1) / 7 = 3.5 / 7 = 0.5. Element 2 = (4 * 3/8 + 3 * 2/3) / 7 = (1.5 + 2) / 7 = 3.5 / 7 = 0.5. Ratio is 1:1.

Multiple choice

A solid floats with $\dfrac{2}{3}$ of its volume immersed in a liquid and with $\dfrac{3}{4}$ of its volume immersed in another liquid. What fraction of its volume will be immersed if it floats in a homogeneous mixture formed of equal volumes of the liquids?
  1. $\dfrac{6}{7}$
  2. $\dfrac{8}{11}$
  3. $\dfrac{11}{16}$
  4. $\dfrac{12}{17}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let V be volume and d be density of solid. d1, d2 are densities of liquids. V_immersed1 = 2/3 V => d = 2/3 d1. V_immersed2 = 3/4 V => d = 3/4 d2. d1 = 3/2 d, d2 = 4/3 d. Mixture density dm = (d1+d2)/2 = (3/2 + 4/3)/2 * d = (17/6)/2 * d = 17/12 d. Fraction immersed = d/dm = 1 / (17/12) = 12/17.

Multiple choice

There is $1000$ litres milk in a pot. $100$ litres of milk is taken out and same amount of water is poured into it. Again $200$ litres of mixture is taken out and same amount of water is poured into it and finally $400$ litres of mixture is taken out and same amount of water is poured into it then what is the amount of milk in the resulting mixture?
  1. $432$
  2. $436$
  3. $425$
  4. $438$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial milk = 1000. After 100 out, 900 left. After 200 out of mixture (20% of 1000), 20% of milk is removed: 900 - 180 = 720. After 400 out of mixture (40% of 1000), 40% of milk is removed: 720 - 288 = 432.