A container contains 100 litres of acid. From the container , 10 litres acid was taken out and replaced by equal amount of water. This process was repeated further twice, then the amount of acid left in the container is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 72.9 litres
Each time 10 litres of the mixture is removed from 100 litres, \( \frac{10}{100} \) of the acid present goes out, so \( \frac{9}{10} \) of it remains. The process is done once and then repeated twice more, 3 times in all:
\( \displaystyle \text{Acid left}=100\left(1-\frac{10}{100}\right)^3 \)
\( \displaystyle =100\times(0.9)^3 \)
\( \displaystyle =100\times 0.729 \)
\( \displaystyle =72.9\ \text{litres} \)
Why the other options are incorrect
Option (1) 70 litres — Incorrect. This subtracts 10 litres of acid each time; after the first step the 10 litres removed contain less than 10 litres of acid.
Option (3) 82.9 litres — Incorrect. \( (0.9)^3=0.729 \), not 0.829.
Option (4) 73.9 litres — Incorrect. \( (0.9)^3=0.729 \), not 0.739.
CBSE Applied Mathematics (Class XII):
Alligation and Mixture
