In a 2025 litre mixture of milk and water, the ratio of milk to water is 12 : 13. To get a new mixture containing milk and water in the ratio of 12 : 15, the amount of water to be added is 

Given:

Initial mixture volume = 2025 litres

Ratio of milk to water = 12 : 13

New ratio of milk to water = 12 : 15

Formula used:

Amount of milk = (Total volume) × (Milk ratio / (Milk ratio + Water ratio))

Amount of water to be added = New water volume - Initial water volume

Calculation:

Initial amount of milk = 2025 × (12 / (12 + 13))

⇒ Initial amount of milk = 2025 × (12 / 25)

⇒ Initial amount of milk = 972 litres

Initial amount of water = 2025 - 972

⇒ Initial amount of water = 1053 litres

In the new mixture, let the total volume be 2025 + x litres (where x is the amount of water to be added)

New amount of water = 1053 + x litres

New ratio of milk to water = 12 / 15

⇒ (972 / (1053 + x)) = 12 / 15

⇒ 972 × 15 = 12 × (1053 + x)

⇒ 14580 = 12636 + 12x

⇒ 14580 - 12636 = 12x

⇒ 1944 = 12x

⇒ x = 1944 / 12

⇒ x = 162 litres

∴ The correct answer is option 2.