Question

An army camp of 250 men has provision for 350 days. After 25 days, 50 men left the camp The food will last for

___ days. (Round off the answer to the nearest integer)

Answer 1

Number of days left = 350 - 25 = 325

Number of men left in the camp = 250 - 50 = 200

Let the number of food last be $x$ for 200 men

Hence Men Days Its in inverse proportion .

250 325

200 $x$

$\therefore$ $\frac{250}{200}$ = $\frac{x}{325}$

Hence $x=\frac{325\times 250}{200}$

= 406.25 days

= 406 days

Alternate Solution
Remaining number of days = (350-25) days = 325 days.

250 men had provisions for 325 days

1 man had provisions for $(250\times 325)$ days

200 men has provisions for $\frac{(250\times 325)}{200}$ days

= 406.25days =406 days

hence, the remaining food will last for 406 days.