How much water should be added to 60 liters of milk at  liters a rupee so as to have a mixture worth  liters a rupee?

Given:

Initial amount of milk = 60 liters

Initial price of milk =  liters per rupee

Desired price of the mixture =  liters per rupee

Formula Used:

Value of milk = Volume of milk / Price

Value of mixture = Volume of mixture / Price

Calculation:

Let the amount of water added be x liters.

Initial value of milk = 60 / (3/2) = 60 × (2/3) = 40 rupees

Total volume of mixture = 60 + x liters

Desired value of mixture = (60 + x) / (15/8) = (60 + x) × (8/15) rupees

Setting the initial value equal to the desired value:

⇒ 40 = (60 + x) × (8/15)

⇒ 40 = (8/15) × (60 + x)

⇒ 40 × 15 = 8 × (60 + x)

⇒ 600 = 480 + 8x

⇒ 8x = 120

⇒ x = 120 / 8

⇒ x = 15 liters

The amount of water to be added is 15 liters.

Shortcut Trick As per question,

Initial:

Cost of 3/2 lt milk = 1 Rs

Cost of 1 lt milk = 1 * (2/3) = 2/3 Rs

Final:

Cost of 15/8 lt of mixture = 1 Rs

Cost of 1 lt of mixture = 8/15 Rs

Cost of water = 0 Rs

Now by using the allegation method, we get

⇒ Milk = 4 unit = 60 lt

⇒ 1 unit = 60/4 = 15 lt

⇒ Water = 1 unit = 15 lt

∴ The amount of water to be added is 15 liters.