Question

A fort has provisions for 60 days. If after 15 days, 500 men strengthen them and the food lasts 40 days longer, how many men are there in the fort (initially)?

• A. 3000
• B. 4000
• C. 5000
• D. 6000
• E. none

Answer 1

The correct option is B

4000

Let there be 'x' men in the beginning so that after 15 days the food for them is left for 45 days.

After adding 500 men the food lasts for only 40 days.

Now (x+500) men can have the same food for 40 days.

Therefore by equating the amount of food we get,

$45\times x=(x+500)\times 40$

$\Rightarrow 45x=(x+500)\times 40$

$\Rightarrow 5x=20,000$

$\Rightarrow x=4,000$

$Thereforethereare4,000meninthefort.$