In a camp of soldiers there was a stock of food for 190 days for 4000 soldiers. After 30 days 800 soldiers left the barrack. For how many days shall the leftover food last for the remaining soldiers?

Question: In a camp of soldiers there was a stock of food for 190 days for 4000 soldiers. After 30 days 800 soldiers left the barrack. For how many days shall the leftover food last for the remaining soldiers?

Solution:
Let, the remaining food last for x days
4000 soldiers had provision for 160 days
3200 soldiers had provision for x days

ATQ,
3200 : 4000 = 160 : x
⇒ 3200x = 4000 × 160
⇒ x = (4000 × 160)/3200
∴ x = 200

The remaining food last for 200 days.