A garrison had provisions 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?

Suppose that y men had provisions for D days .Then y men had provisions for ( D - 10 ) days .
[ y - ( y/5 ) ] men had provisions for D days .
According to question ,
∴ y( D - 10 ) = ( 4y/5 ) x D ⇒ 5Dy - 50y = 4Dy
⇒ Dy - 50y = 0 ⇒ y( D - 50 ) = 0 ⇒ D = 50 days
Hence required answer is 50 days .