Three pipes A, B and C can fill a cistern in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill it in 7 hours. The time taken by C alone to fill the cistern is?

Part filled in 2 hours = 2 x 1/6 = 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 = (2/3 x 1/7) = 2/21
(A + B + C)'s 1 hour's work = 1/6
C's 1 hours work = (1/6 - 2/21) = 1/14
Hence, C alone can fill the cistern in 14 hours.