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A container contains certain quantity of milk. Malik sold 20% of the milk from the container and added same quantity of water to it. From this mixture, 40% of the quantity was sold to local dealer. After this Malik again added water to the mixture equivalent to 18% of the quantity, he sold to the local dealer. At the end, he sold 75% of the mixture to the dairy and remaining unsold quantity was 5 liter. What was the initial quantity of milk in the container (approx.)?

A container contains certain quantity of milk. Malik sold 20% of the milk from the container and added same quantity of water to it. From this mixture, 40% of the quantity was sold to local dealer. After this Malik again added water to the mixture equivalent to 18% of the quantity, he sold to the local dealer. At the end, he sold 75% of the mixture to the dairy and remaining unsold quantity was 5 liter. What was the initial quantity of milk in the container (approx.)? Correct Answer 30 litre

Let the initial quantity of milk = ‘x’ liter

Quantity of the milk left after selling 20% of the initial quantity = x - (20% of x) = x - 0.2x = 0.8x

If Malik adds 20% water is added to the milk, the final quantity will still remain same

Ratio of milk to water in ‘x’ liter of solution = (0.8x/0.2x) = 8/2 = 4 ∶ 1

Quantity of mixture left after selling to the local dealer = x - (40% of x) = x - 0.4x = 0.6x

Extra amount of water which was added to the mixture = 18% of quantity that was sold

⇒ 0.18 × 0.4x

⇒ 0.072x

Total quantity of mixture = 0.6x + 0.072x = 0.672x

Given 75% of this mixture was sold to dairy,

then the remaining quantity in the container = 0.672x - (75% of 0.672x) = 0.672x - 0.504x = 0.168x

Remaining quantity = 5 liter

⇒ 0.168x = 5

⇒ x = (5/0.168)

⇒ x = 29.76 ≈ 30 litres (approximately)

∴ Initial quantity(x) = 30 litres

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