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 6 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 6 hours. The number of hours taken by C alone to fill the tank is

Solution:
A, B and C together can fill in one hour = 1/6
in two hours = 2/6 = 1/3

the remaining part is = 1 - 1/3 = 2/3

in 6 hours, A and B can do = 2/3
so, in one hour A and B can do = 2/(3 × 6) = 2/18

so, C can do in one hour = (A, B and C in one hour) - (A and B in one hour)
= 1/6 - 2/18
= 1/18

hence, C take 18 hours to fill the tank