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

The Correct Option is A

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 that 50% of the new solution is acid: 

\[ \frac{y}{x + 2} = 0.5 \]

After adding 15 liters of acid, the solution becomes:

Water: \( x + 2 \), Acid: \( y + 15 \)

Given that 80% of the final solution is acid:

\[ \frac{y + 15}{x + 2 + 15} = 0.8 \]

Solving these two equations, we get:

\[ x = 2, \quad y = 7 \]

Therefore, the ratio of water to acid in the original solution is \( 2 : 7 \) or \( 1 : 3.5 \).