Question

4 litres are drawn from a container full of milk and then is filled with water. This operation is performed three more times. The ratio of the quantity of milk left in the container and that of water at the end is 16:65. How much milk did the container hold initially?

• A. 24 L
• B. 12 L
• C. 15 L
• D. 25 L

Answer 1

The correct option is B 12 L

Suppose a container contains M units of mixture of ‘A’ and ‘B’. From this, R units of mixture is taken out and replaced by an equal amount of ingredient B only. This process (of taking out and replacing it) is repeated ‘n’ times, then, after ‘n’ operations, Amount of ‘A’ left/Amount of ‘A’ originally
present $={(1–\frac{R}{M})}^n$
R = 4 litres; $n=4\text{and}M=?\frac{16}{81}={(1-\frac{4}{M})}^4={\left(\frac{2}{3}\right)}^4$
Therefore, $\left(\frac{4}{M}\right)=\frac{1}{3}\Rightarrow M=12L$