A container contains $40$ litres of milk. From this container $4$ litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?

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Solution

Suppose a container contains x units of a liquid from which y units are taken out and replaced by water. After n operations, quantity of pure liquid
$= x (1 - \frac{y}{x})^{n}$ units.
milk contained by the container now
$= 40 (1 - \frac{4}{40})^{3}$
$= 40 (1 - \frac{1}{10})^{3}$
$= 40 \times \frac{9}{10} \times \frac{9}{10} \times \frac{9}{10}$
$= \frac{4 \times 9 \times 9 \times 9}{100}$
$= 29.16$

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A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?

Suppose a container contains x units of a liquid from which y units are taken out and replaced by water. After n operations, quantity of pure liquid=x(1−yx)n units.milk contained by the container now=40(1−440)3=40(1−110)3=40×910×910×910=4×9×9×9100=29.16

A container contains $40$ litres of milk. From this container $4$ litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?