How many liters of oil at Rs.40 per liter should be mixed with 240 liters of a second variety of oil at Rs.60 per liter so as to get a maximum whose cost is Rs.52 per liter?

Let the quantity of first oil (Rs. 40/litre) to be mixed be x litres.

Given:

• Cost of 1st variety = Rs. 40/litre
• Cost of 2nd variety = Rs. 60/litre
• Quantity of 2nd variety = 240 litres
• Cost of mixture = Rs. 52/litre

Apply alligation rule:

Cheaper          = 40
                          \
                           \
                            >     52
                           /
                          /
Dearer           = 60

Difference between the rates:

• 60 - 52 = 8 (parts of cheaper oil)
• 52 - 40 = 12 (parts of dearer oil)

So, the ratio of 1st oil : 2nd oil = 8 : 12 = 2 : 3

Quantity of 2nd oil is 240 litres (3 parts)

⇒ 1 part = 240 / 3 = 80 litres

⇒ Quantity of 1st oil (2 parts) = 80 × 2 = 160 litres

Answer: 160 litres of oil at Rs. 40/litre should be mixed.