Question

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

Answer 1

Let original number of men in the fort = "x".
(food in fort)/x = 42 days
(f)/42 = x
=>f=42x ………………(1)

After 10 days:
Amt of original food remaining = (32/42)(f) = (16/21)f

Equation:
(16/21)(f)/(x+200) = 24

Substitute for (f) from (1), solving for "x":
(16/21)(42x)/(x+200) = 24

16(2x) = 24x + 4800
32x = 24x + 4800
8x = 4800
x = 600 men