Three pipes A, B and C can fill a tank in 8 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 9 hours. The number of hours taken by C alone to fill the tank is?

Question: Three pipes A, B and C can fill a tank in 8 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 9 hours. The number of hours taken by C alone to fill the tank is?

Solution:
Part filled in 2 hours = 2/8 = 1/4
Remaining part = 1 - (1/4) = 3/4

(A + B)'s 9 hour's work = 3/4
(A + B)'s 1 hour's work = 3/36 = 1/12

∴ C's 1 hour's work = {(A + B + C)'s 1 hour's work } - {(A + B)'s 1 hour's work }
= (1/8) - (1/12)
= (3 - 2)/24
= 1/24
∴ C alone can fill the tank in 24 hours.