Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 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 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is-

Solution:
Part filled in 2 hours = 2/6 = 1/3
Remaining part =(1 - 1/3) = 2/3

(A + B)'s 7 hour's work = 2/3
(A + B)'s 1 hour's work = 2/21

C's 1 hour's work = {(A + B + C)'s 1 hour's work } - { (A + B)'s 1 hour's work }
= 1/6 - 2/21
= (7 - 4)/42
= 1/14
∴ C alone can fill the tank in 14 hours.