A milkman has 100 liters of pure milk. ’a’ liters of milk is taken out and sold at 37.5% more than the cost price of the milk

Q. A milkman has 100 liters of pure milk. ’a’ liters of milk is taken out and sold at 37.5% more than the cost price of the milk. After that ‘37.5a%’ liters of water are added to the remaining milk. Then the remaining quantity of the mixture is sold at 33.33℅ less than the cost price of the milk. The ratio of the selling price of ‘a’ liters of milk and the remaining mixture is 11: 10 and the cost price of the pure milk is 0.6a. Find the difference between ‘a’ liters of milk and added water?

A. 30 liters

B. 20 liters

C. 15 liters

D. 35 liters

E. None of these

Sol:

Initially pure milk = 100 liters

‘a’ liters of milk is taken out after that Remaining

milk is 100 – a

37.5a℅ of water added to the remaining mixture

which is 3a/8

So, 100 – a + 3a/8 => (800 – 5a)/8 liters

Cost Price of the pure milk =0.6a= 3a/5.

‘a’ liters of the milk is sold at 37.5℅ above the cp

of milk

So, 3a/5 * 11/8 = 33a/40

Selling price of ‘a’ litres of milk = a * 33a/40 =>

33a2/40

And the remaining quantity is sold at 2/3 of cp of

milk

= 3a/5 * 2/3 => 2a/5

Selling price of the remaining quantity = ((800 –

5a) / 8) * (2a/5) = (800a – 5a2/20)

33a2/40 = 11

800a-5a2/20 = 10

3a2/40 * 20/800a-5a2 = 1/10

a = 40

Required difference = 40 – 3/8(40) = 25 litres