Question

A container originally contains 10 litres of pure spirit. From this container 1 litre of spirit is replaced with 1 litre of water. Subsequently, 1 litre of the mixture is again replaced with 1 litre of water and this process is repeated one more time. How much spirit is now left in the container?

1. 7.58 litres
2. 7.84 litres
3. 7 litres
4. 7.29 litres

Answer 1

Correct Answer - Option 4 : 7.29 litres

Concept:

\({\bf{Volume}}\;{\bf{of}}\;{\bf{liquid}}\;{\bf{left}} = {\bf{x}}{\left( {\frac{{{\bf{x}} - 1}}{{\bf{x}}}} \right)^{\bf{n}}}\)

where x = Original amount of liquid, n = Number of times replaced.

Calculation:

Given:

x = 10 litre, n = 3

Now, we know that

\({\bf{Volume}}\;{\bf{of}}\;{\bf{spirit}}\;{\bf{left}} = {\bf{x}}{\left( {\frac{{{\bf{x}} - 1}}{{\bf{x}}}} \right)^{\bf{n}}}\)

∴  Volume of spirit left = \(10{\left( {\frac{{10 - 1}}{{10}}} \right)^3} = \frac{{729}}{{100}} = 7.29\)  litres