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 of the container be $V$ litres.
Milk remaining after one replacement:
$\frac{V-10}{V}$
Milk remaining after second replacement:
$\left(\frac{V-10}{V}\right)^{2}$
Final milk : water = $4:5$
Total = 9 parts → milk = $\frac{4}{9}V$
So,
$V\left(\frac{V-10}{V}\right)^{2}=\frac{4}{9}V$
Cancel $V$:
$\left(\frac{V-10}{V}\right)^{2}=\frac{4}{9}$
Take square root:
$\frac{V-10}{V}=\frac{2}{3}$
$3(V-10)=2V$
$3V-30=2V$
$V=30$
Capacity = 30 litres