# In 144 litres pure milk, 16 liters of milk is replaced by water and if this process is repeated two more times, then find the quantity of milk in the

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In 144 litres pure milk, 16 liters of milk is replaced by water and if this process is repeated two more times, then find the quantity of milk in the final mixture.
1. 101
2. 101.13
3. 205.03
4. 113.7

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Correct Answer - Option 2 : 101.13

Given:

Quantity of pure milk = 144 liters

16 liters of milk is replaced by water 3 times.

Formula used:

Suppose a container contains A units of a liquid from which B units are taken out and replaced by water.

After n operations, operations, operations,

Quantity of pure liquid in the final mixture = A {1 – (B/A)}n

Calculation:

According to the question,

Quantity of pure milk in the final mixture = A {1 – (B/A)}n

⇒ 144 × {1 – (16/144)}3

⇒ 144 × {1 – (1/9)}3

⇒ 144 × (8/9)]3

⇒ 144 × (512/729)

⇒ 101.13

∴ The final quantity of the milk is 101.13 liters.