Question

From the 50 litres of milk, 5 litres of milk is taken out and after it, 5 litres of water is added to the rest amount of milk. Again 5 litres of the mixture of milk and water is drawn out and it was replaced by 5 litres of water. If this process is continued similarly for the third time, the amount of milk left after the third replacement:

• A. 45 L
• B. 36.45 L
• C. 40.5 L
• D. 42.5L

Answer 1

The correct option is B 36.45 L

This question can be interpreted as there is a dilution of 10% (5L from 50L) every time.
Hence, amount of milk left after the third replacement = $50\times (0.9{)}^3=36.45L$

Conventional Approach:


Shortcut:
$50\times (1-\frac{5}{50})\times (1-\frac{5}{50})\times (1-\frac{5}{50})$
$=50\times \frac{45}{50}\times \frac{45}{50}\times \frac{45}{50}=50\times {\left(\frac{45}{50}\right)}^3=50\times {\left(\frac{9}{10}\right)}^3$
= 36.45 L