CAT 2025 Slot 3 · Quant · Question 22

Let v litres be moved each time. Vessel A loses v and later gains v, so it ends with 60 litres again.

The v litres poured into B are pure alcohol, so B then holds 60+v litres of which v is alcohol and 60 is water.

After stirring, the fraction of water in B is \frac{60}{60+v}.

The v litres returned to A therefore carry \frac{60v}{60+v} litres of water — and this is the only water A ever receives.

The final ratio in A is 15:4, so water makes up \frac{4}{19} of its 60 litres, that is \frac{240}{19} litres.

Equating, \frac{60v}{60+v}=\frac{240}{19}.

Cross-multiplying, 1140v=240\left( 60+v \right), so 1140v=14400+240v.

That gives 900v=14400 and v=16 litres.

Shortcut. Track only the water. A starts with none, and the single transfer back is its only source, so one equation in v settles the question — the alcohol never needs following.