Question : 40 litres of milk are kept in a container. 4 litres of milk were removed from this container and replaced with water. This procedure was performed two more times. How much milk does the container now hold?
Option 1: 30 litres
Option 2: 34.23 litres
Option 3: 29.16 litres
Option 4: 32 litres
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Correct Answer: 29.16 litres
Solution :
Suppose a container contains $a$ units of a liquid from which $b$ units are taken out and replaced by water, after $n$ number of operations,
The quantity of pure liquid in the final mixture = $a[1-\frac{b}{a}]^n$
Here, $a$ = 40 litres, $b$ = 4 litres and $n$ = 3
So, the required amount of milk
= $40[1-\frac{4}{40}]^3$
= $40×\frac{9}{10}×\frac{9}{10}×\frac{9}{10}$
= $\frac{2916}{100}$
= $29.16$ litres
Hence, the correct answer is 29.16 litres.
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