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 this new solution, the final solution had 80% acid concentration. The ratio of water and acid in the original solution was

• A. 3 : 5
• B. 5 : 3
• C. 4 : 5
• D. 5 : 4

Answer 1

Answer: (A)

3 : 5

Answer 2

Let the original solution have $x$ liters of water and $y$ liters of acid.

After adding 2 liters of water, the solution has $(x+2)$ liters of water and $y$ liters of acid.

Given, 50 percent of the new solution is acid. So, $\frac{y}{(x+2)} = 0.5$.

After adding 15 liters of acid, the solution has $(x+2)$ liters of water and $(y+15)$ liters of acid. Given, 80 percent of the final solution is acid. So, $\frac{(y+15)}{(x+2+15)} = 0.8$.

Solving these two equations, we get $x = 2$ and $y = 7$.

Therefore, the ratio of water and acid in the original solution is 2:7 or 1:3.5.