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

12 litres

The correct answer is Option (1) - 12 litres

$\text{Cost of milk per litre} = \frac{120}{2.5} = 48$

$\text{Water is free (cost } = 0)$

$\text{Let water added} = x \text{ litres}$

$\text{Total cost} = 36 \times 48 = 1728$

$\text{Total volume} = 36 + x$

$\text{Mean price} = 36$

$36 = \frac{1728}{36 + x}$

$36(36 + x) = 1728$

$1296 + 36x = 1728$

$36x = 432$

$x = 12$

The quantity of water to be added is $12$ litres.