Question

Vessels A and B contain 60 litres of alcohol and 60 litres of water, respectively. A certain volume is taken out from A and poured into B. After stirring, the same volume is taken out from B and poured into A. If the resultant ratio of alcohol and water in A is 15 : 4, then the volume, in litres, initially taken out from A is

Hint:

In transfer-and-mix problems, track the \emph{fraction} of each component after mixing, then multiply by the transferred volume. Ratios often simplify nicely when common denominators cancel.

Answer 1

Correct Answer: 16

Step 1: Take out \( x \) litres of pure alcohol from A and pour into B. Vessel B now has \( x \) litres alcohol and 60 litres water, total \( (60+x) \) litres.
Step 2: Take out \( x \) litres from this mixture in B. It contains alcohol \( = \frac{x^2}{60+x} \) and water \( = \frac{60x}{60+x} \).
Step 3: Pour this back into A. A now has alcohol \( = (60-x) + \frac{x^2}{60+x} = \frac{3600}{60+x} \) and water \( = \frac{60x}{60+x} \). Given the ratio is \( 15:4 \), so \( \frac{3600}{60x} = \frac{15}{4} \), giving \( x = 16 \).
\[ \boxed{x = 16 \text{ litres}} \]