A milk man has a mixture of milk in which ratio of milk and water is 5 : 3.

Ques - A milk man has a mixture of milk in which ratio of milk and water is 5 : 3. He sells 40 litres of milk i.e. mixture then he adds up 15 litres of pure water. Now the ratio of milk and water is 5 : 4. What is the new quantity of mixture? 

(a) 72 litres

(b) 270 litres

(c) 135 litres

(d) Data insufficient 

Solution - 

Ratio of milk and water = 5 : 3

Let,

Milk in the mixture = 5x

Water in the mixture = 3x

Total Mixture = 8x

He sells 40 litres of mixture of milk.

After selling 40 litres of mixture. He has,

Quantity of milk = 5x - (5/8) of 40 litres

= 5x - (5/8) × 40

= (5x - 25) litres

Quantity of Water = 3x - (3/8) of 40 litres

= 3x - (3/8) × 40

= (3x - 15) litres

Then,

He adds up 15 litres of pure water.

New quantity of water = (3x - 15) + 15

= 3x

But,

The ratio of milk and water is 5 : 4 (given).

Therefore,

Milk/water = 5/4

(5x - 25)/3x = 5/4

(20x - 100) = 15x

5x = 100

x = 20

Thus,

The quantity of Mixture of milk and water = 5x - 25 + 3x

= 8x - 25

= 8(20) - 25

= 160 - 25

= 135

Therefore,

The new quantity of mixture is = 135 litres.

Hence,

The correct answer is option (c) 135 litres. 

Thank You