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 processes is repeated one more time. How much spirit is now left in the container?

• A. 7.58 litres
• B. 7.84 litres
• C. 7 litres
• D. 7.29 litres

Answer 1

The correct option is D 7.29 litres

Shortcut Method:

Every time if we take 1 litre of mixture out and replace with water, content of pure spirit will keep on reducing by 10%.

So, final quantity of spirit after 3 such operations are
$10\times 0.9\times 0.9\times 0.9=7.29litres$

Alternate solutions:

$\frac{Quantityofspiritleftafter{n}^{th}operation}{Initialquantityofspirit}$

$={\left(\frac{a-b}{a}\right)}^n={(1-\frac{b}{a})}^n$

Where 'a' is an initial quantity of pure spirit and 'b' is quantity taken out and replaced every time. Hence, quantity of spirit left after $3^{rd}$ operation.

$=initialquantity\times {(1-\frac{1}{10})}^3=10\times 0.9\times 0.9\times 0.9=7.29litres$