A vessel is full of 80 litres of milk. 16 litres of milk is taken out and replaced by the same amount of water. Then 10 litres of the mixture is taken out and replaced by the same amount of water. How much water is in the vessel at the end of the second process?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 24 litres
Each draw removes the same fraction of the milk that it removes of the whole vessel; the volume stays the same.
After the first draw: milk \(=80-16=64\) litres
The second draw removes \(\frac{10}{80}\) of the milk: milk \(=64\times\frac{70}{80}=56\) litres
Water \(=80-56=24\) litres
The vessel now has 24 litres of water.
Why the other options are incorrect
Option (1) 56 litres — Incorrect. This is the milk left, not the water.
Option (3) 26 litres — Incorrect. This is the total drawn off; the second draw takes out some water as well as milk.
Option (4) 16 litres — Incorrect. This takes the second draw as removing only water, so the water would stay at 16 litres.