Question

From a jar of wine containing 32 litres, 4 litres is drawn out, and the jar is filled up with water. If the same proportion of wine is further drawn out two more times, what proportion of wine to water will be there in the resulting mixture?

Accepted Answer

B. Fraction of wine retained in each step = $1 - \frac{4}{32} = \frac{7}{8}$. After 3 operations, wine remaining = $32 	imes (\frac{7}{8})^3 = 32 	imes \frac{343}{512} = \frac{343}{16} = 21.4375$ litres. Water remaining = $32 - 21.4375 = 10.5625$ litres. Ratio of wine to water = $\frac{21.4375}{10.5625} = \frac{343}{169}$.

Repeated replacement of wine

Explanation

Practise this under exam conditions