CAT 2024 Slot 2 QA Question 12: 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 th

Question

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 th

Accepted Answer

Work backwards from the $50\%$ solution.
After adding $2$ litres of water, let the solution contain $t$ litres of acid and $t$ litres of water.
After adding $15$ litres of acid, acid becomes $t + 15$ and total solution becomes $2t + 15$.
$\dfrac{t+15}{2t+15} = \dfrac{4}{5}$
$\Rightarrow 5t + 75 = 8t