Question

A fort provisioned for 42 days, after 10 days, a reinforcement of 200 men arrives and the food will now last for 24 more days. How many men were there in the fort?

Answer 1

Let there be N men in the fort initially.
Let one person eat an amount equal to V in a day.

So we have a total amount of food = 42 * V * N

In 10 days, food consumed = 10 * V * V

After 10 days food amount remaining, 32 V N

Number of men now = N + 200.

Food lasts 24 days: ie., food amount = 24 *V * (N + 200)

=> 32 V N = 24 * V * (N+200)
=> 32 N = 24 N + 4800
=> N = 600

There were 600 persons.