From a container full of milk, 10 liters (\(l\)) was drawn and replaced by water. This process is repeated one more time. The ratio of quantity of milk and water left in the container is 4:5. Then the capacity of the container is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(30l\)
Let the capacity be C litres. Each time 10 litres of the mixture are drawn and replaced by water, the milk left is multiplied by \(1 - \frac{10}{C}\) (repeated replacement). After two operations:
\( \displaystyle \text{Milk left} = C\left(1 - \frac{10}{C}\right)^2 \)
Milk : water = 4 : 5, so the milk is \(\frac{4}{9}\) of the container:
\( \displaystyle \left(1 - \frac{10}{C}\right)^2 = \frac{4}{9} \)
\( \displaystyle 1 - \frac{10}{C} = \frac{2}{3} \)
\( \displaystyle \frac{10}{C} = \frac{1}{3} \)
\( C = 30 \text{ litres} \)