Question

A can contains a mixture of two liquids, A and B in the ratio 7 : 5. When 9 litres of mixture is drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially ?

• A. 14
• B. 21
• C. 35
• D. 28
• E. 20

Hint:

In mixture problems, track the quantity of each component separately. Use fractions to avoid decimals.

Answer 1

The Correct Option is B

Step 1: Let initial quantity = $7x + 5x = 12x$ litres. A = $7x$, B = $5x$.
Step 2: 9 litres drawn off. In the drawn mixture, A = $\frac{7}{12} \times 9 = \frac{63}{12} = 5.25$ litres, B = $9 - 5.25 = 3.75$ litres.
Step 3: Remaining: A = $7x - 5.25$, B = $5x - 3.75$.
Step 4: Add 9 litres of B. New B = $5x - 3.75 + 9 = 5x + 5.25$.
Step 5: New ratio A:B = $ (7x - 5.25) : (5x + 5.25) = 7 : 9$.
Step 6: Cross multiply: $9(7x - 5.25) = 7(5x + 5.25)$. $63x - 47.25 = 35x + 36.75$. $28x = 84 \implies x = 3$.
Step 7: Initial A = $7x = 21$ litres.
Step 8: Final Answer: 21.