CAT 2024 Slot 2 · Quant · Question 19

CAT 2024 Slot 2 previous year question on Averages, Mixture and Alligation, with the answer and a step-by-step solution.

Averages, Mixture and AlligationArithmeticMultiple choiceMedium
A vessel contained a certain amount of a solution of acid and water. When 2 litres of water was added to it, the new solution had 50% acid concentration. When 15 litres of acid was further added to this new solution, the final solution had 80% acid concentration. The ratio of water and acid in the original solution was
  1. A
    5 : 3
  2. B
    4 : 5
  3. C
    5 : 4
  4. D
    3 : 5
Pick an option, then check.
Answer & solution

Answer: Option D

Let the original solution contain a litres of acid and w litres of water.

Adding 2 litres of water leaves the acid at a and raises the water to w+2.

A 50% acid concentration means the two are equal, so a=w+2.

Adding 15 litres of acid raises the acid to a+15, while the water stays at w+2.

An 80% acid concentration means acid is four times the water, so a+15=4\left( w+2 \right).

But w+2=a from the first condition, so a+15=4a.

That gives 3a=15 and a=5.

Then w=a-2=3.

The ratio of water to acid in the original solution is 3:5, the fourth option.

Shortcut. At 50% the acid equals the water, so the whole second condition can be written in terms of acid alone: a+15=4a. One equation and one unknown, with the water read off afterwards. Note the question asks for water : acid, not acid : water.

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