The quantity of water that must be added to 24 litres of milk at $2\frac{1}{2}$ litres for Rs. 120 so as to have mixture worth Rs. 36 a litre is :

8 litres

The correct answer is Option (1) → 8 litres

Price per liter = $\frac{Cost}{Quantity}=\frac{120}{\frac{5}{2}}=\frac{120×2}{5}=48$

The equation for the weighted average,

$\frac{Total\,cost\,of\,milk}{Total\,volume\,of\,mixture}=36$

$⇒24×48=1152$

Total volume of mixture,

$24+x$

$⇒\frac{1152}{24+x}=36$

$⇒x=\frac{288}{36}=8L$