From a drum filled with 48 litres of soya milk, 12 litres of soya milk was taken out and replaced by an equal amount of cow milk. The process was further repeated twice. How much soya milk is left in the drum now?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 20.25 litres
Each time 12 litres of the mixture are taken out of 48 litres, a fraction \( \frac{12}{48}=\frac{1}{4} \) of the soya milk present is removed, so \( \frac{3}{4} \) of it stays. The process is done once and then repeated twice, that is, 3 times in all.
\( \displaystyle \text{Soya milk left}=48\left(1-\frac{12}{48}\right)^3 \)
\( \displaystyle =48\times\left(\frac{3}{4}\right)^3 \)
\( \displaystyle =48\times\frac{27}{64} \)
\( \displaystyle =20.25\ \text{litres} \)
CBSE Applied Mathematics (Class XII):
Alligation and Mixture
