A barrel contains a mixture of wine and water in the ratio 3:1. How much fraction of the mixture must be drawn off and substitute…

Question

A barrel contains a mixture of wine and water in the ratio 3:1. How much fraction of the mixture must be drawn off and substituted by water so that the ratio becomes 1:1?

1. A. 1/2
2. B. 1/3 (Correct answer)
3. C. 1/4
4. D. 2/3

Correct Answer

Option B — B

Detailed Solution & Explanation

The correct answer is Option B.

Key Points

• Start with wine : water = 3 : 1, so in 4 parts, wine = 3/4 of the mixture.
• We want the final ratio 1 : 1, i.e. wine = 1/2.
• Let fraction f be drawn off and replaced with water.
• Drawing off f removes wine in proportion, so remaining wine fraction = (3/4)(1 − f). Set this equal to 1/2:
• (3/4)(1 − f) = 1/2
• 1 − f = 2/3
• f = 1/3.
• So 1/3 of the mixture must be replaced with water.

Exam Tip

• when a fraction f is drawn and replaced by water, the wine left = initial-wine-fraction × (1 − f).
• Set it to the target and solve.

Additional Information

• Replacement problems are handled by tracking the component that is not added. Wine starts at 3/4 of the mixture; after removing fraction f and replacing with water, wine becomes (3/4)(1 − f).
• Set that equal to the target proportion and solve for f.
• The repeated-replacement formula is worth memorising: after n operations the original quantity left is A(1 − f)ⁿ.