Question

A vessel contained a solution of acid and water in which water was 64%. Four litres of the solution were taken out of the vessel and the same quantity of water was added. If the resulting solution contained 30% acid, then the quantity (in litres) of the solution, in the beginning in the vessel, was:

• A. 32
• B. 30
• C. 24
• D. 20

Hint:

In such problems, use the percentage of the acid and water content before and after the operation, and form equations based on the principle of conservation of the amount of acid.

Answer 1

The Correct Option is C

Let the total quantity of the solution initially in the vessel be \(x\) litres. The amount of acid in the solution is \(0.36x\) and the amount of water is \(0.64x\). After taking out 4 litres of the solution, the remaining solution in the vessel will contain \(x - 4\) litres. Then, after adding 4 litres of water, the total volume is \(x\) again. The amount of acid remains unchanged, but now the amount of acid in the new solution is \(0.30 \times x\). By setting up an equation based on the concentration of acid in the new solution, we solve for \(x = 24\).
Thus, the correct answer is 24.