A military camp had enough food supplies to last for a certain number of days. After 10 days, 1/5 of the men desert and it is found that the provisions will now last just as long as before. How long was that?

Question: A military camp had enough food supplies to last for a certain number of days. After 10 days, 1/5 of the men desert and it is found that the provisions will now last just as long as before. How long was that?

Solution:
Let, initially there be 'x' men having foods for y days
After 1/5 of the men left = x - (x/5)
= 4x/5

After 10 days,
x men had foods for (y - 10) days
∴ 1 man had foods for x(y - 10) days
∴ 4x/5 men had foods for = {5x(y - 10)}/4x days
= 5(y - 10)/4 days

ATQ,
5(y - 10)/4 = y
⇒ 5y - 50 = 4y
∴ y = 50