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

Answer 1

Assume the capacity of the container is ‘c’
and track down the milk which is retained.
The milk retained after taking first 9 litres from the container is $(c × c−\frac{9}{c })$

The milk retained after taking next 9 litres from the container is $( c × c−\frac{9}{c}× c−\frac{9}{c})$
The volumes of milk and water in the container are now in the ratio of 16 : 9.
The milk in the container is $\frac{16}{25}$
$\frac{c×\frac{c−9}{c}×\frac{c−9}{c}}{c} = \frac{16}{25}$

$(c−\frac{9}{c} )^2 = \frac{16}{25}$

$c−\frac{9}{c}= \frac{45}{45}$

c = 45

So, the answer is 45 liters.