A container contains 100 liters of milk. From this container, 10 liters of milk is taken out and replaced by water. This process is repeated two more times. The amount of milk left in the container now is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 72.9 liters
Each time 10 liters of the mixture are taken out of 100 liters and replaced with water, the milk left is \(\frac{90}{100}\) of the milk before. The process is done 3 times in all (once, and then two more times), so by the repeated replacement rule:
\( \displaystyle \text{Milk left} = 100\left(1 - \frac{10}{100}\right)^3 \)
\( = 100 \times (0.9)^3 \)
\( = 100 \times 0.729 = 72.9 \text{ liters} \)
CBSE Applied Mathematics (Class XII):
Alligation and Mixture
