cat 2021 Question 4

Question

From a container filled with milk, 9 litres of milk are drawn and replaced with water. Next, from the same container, 9 litres are drawn and again replaced with water. If the volumes of milk and water in the container are now in the ratio of 16 : 9, then the capacity of the container, in litres, is

Accepted Answer

Let initial volume be $V$, final be $F$ for milk.

The formula is given by : $F = V \cdot (1 - \frac{K}{V})^n$

$n$ is the number of times the milk is drawn and replaced.

so we get $F = V (1 - \frac{K}{V})^2$

here $K = 9$

we get

$\frac{16}{25}V = V \left(1 - \frac{9}{V} ight)^2$

we get $1 - \frac{9}{V} = \frac{4}{5}$ or $-\frac{4}{5}$

If considering $1 - \frac{9}{V} = -\frac{4}{5}$

$V = 5$, but this is not possible because 9 liters is drawn every time.

Hence : $1 - \frac{9}{V} = \frac{4}{5}$, $V = 45 ext{ liters}$

Question 4.

Question Explanation