Question

A garrison of 400men had food for 40days.After 10 days,200 more men joined them .How long will the food last now?(Assume that the food taken by each man is almost the same.​

Answer 1

Let $x$ be the amount of food needed for one man for one day. At the beginning, we have enough food for 400 men for 40 days, i.e.

$400\cdot 40\cdot x = 16000x$

After 10 days, the 400 men will have consumed

$400\cdot 10\cdot x = 4000x$

food, impliying that the food remaining is

$16000x-4000x=12000x$

If 200 more men join the garrison, there are now 600 men. Each of them requires $x$ food each day, and there are $12000x$ units of food remaining. They will last

$\dfrac{12000x}{600}=20$ days.