Question

A vessel contains 16 litres of pure spirit. From this vessel 2 litres of spirit is replaced with 2 litre of water. Subsequently, 2 litres of the mixture is again replaced with 2 litres of'water and this process is repeated one more time. How much spirit is now left in the vessel?​

Answer 1

The volume of spirit left in the vessel is 10.7l.

Given:-

The volume of Pure spirit (v) = 16l

The volume of water replaced (vw) = 2l

The process is repeated = 3 times

To Find:-

The volume of spirit left in the vessel.

Solution:-

You can simply find out the volume of spirit left in the vessel by using the following procedure.

As

The volume of Pure spirit (v) = 16l

The volume of water replaced (vw) = 2l

The process is repeated = 3 times

The volume of spirit left in the vessel (vs) =?

According to the formula,

The volume of spirit left in the vessel =

$vs = v( { \frac{v - vw}{v} )}^{3}$

$vs = 16 \times ( { \frac{16 - 2}{16}) }^{3}$

$vs = 16 \times { (\frac{14}{16}) }^{3}$

$vs = 16 \times \frac{2744}{4096}$

$vs = \frac{43904}{4096}$

$vs = 10.7l$

Hence, The volume of spirit left in the vessel is 10.7l.

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