A camp of soldiers has food for 200 days. After 20 days, 100 more soldiers join the camp and the food now can last for 80 days. What was the initial number of soldiers in the camp?

80

Let number of soldiers be m.

Total available food = m × 200

Food consumed by m soldiers in 20 days = m × 20

Now, 100 soldiers are added to camp,

New number of soldiers = (m + 100)

Now rest food is finished in 80 days by (m + 100) soldiers

food consumed in 80 days = (m + 100) × 80

According to question -

= 200m = 20m + 80(m + 100)

= 200m = 100m + 8000

= 100m = 8000

m = 80