Question:
A garrison of 900 men had provisions for 42 days. However, a reinforcement of 500 men arrived. For how many days will the food last now?
Solution:
Let x be the required number of days. Then, we have:
| No. of men | 900 | 1400 |
| No. of days | 42 | x |
Clearly, more men will take less number of days to finish the food.
So, it is a case of inverse proportion.
Now, $900 \times 42=1400 \times x$
$\Rightarrow x=\frac{900 \times 42}{1400}$
$\Rightarrow x=27$
Therefore, the food will now last for 27 days.