A fort has provisions for 150 men for 45 days. After 10 days 25 men left the fort. How long will the provisions last at the same rate for the remaining men?

Correct option is C

Given:

Provisions for 150 men for 45 days.

After 10 days, 25 men left the fort.

Concept Used:

Total man-days of provisions =$$\text{Number of men} \times \text{Number of days}$$

Solution:​

Total man-days of provisions = 150 × 45 = 6750 man-days

In the first 10 days, the provisions were used by 150 men =  150 × 10 = 1500 man-days used

After 10 days, the remaining provisions are = 6750 − 1500 = 5250 man-days remaining

After 25 men leave, the remaining number of men = 150 − 25 = 125 men

Let the number of remaining days be D. The remaining provisions for 125 men will last for D days, so:

125 × D = 5250

D $$= \frac{5250}{125} = 42 \text{ days}$$​

The provisions will last for 42 days for the remaining 125 men.