A container holds 50 litres of pure alcohol. 10 litres are taken out and replaced by water. The same is done once more with the mixture. How many litres of alcohol are now left in the container?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 32 litres
Each time 10 litres out of 50 litres are taken out, \(\frac{1}{5}\) of the alcohol present goes out, so \(\frac{4}{5}\) of the alcohol remains after every operation.
After the first operation: \(50 \times \frac{4}{5} = 40\) litres
After the second operation: \(40 \times \frac{4}{5} = 32\) litres
So 32 litres of alcohol are left.
Why the other options are incorrect
Option (2) 30 litres — Incorrect. This subtracts 10 litres of alcohol twice. In the second operation the 10 litres taken out are a mixture with only 8 litres of alcohol.
Option (3) 34 litres — Incorrect. The alcohol left is \(50 \times \left(\frac{4}{5}\right)^{2} = 32\) litres, not 34.
Option (4) 40 litres — Incorrect. This is the alcohol after the first operation only.