Pipes A, B and C together can fill a cistern in 12 hours. All the three pipes are opened together for 4 hours and then C is closed. A and B together take 10 hours to fill the remaining part of the cistern. C alone will fill two-thirds of the cistern in:

Given that A, B, C together can fill a cistern   = 12 hours

then (A+B+C ) can fill the tank = $$\dfrac {1}{12}$$

A+B+C all three pipe opened together for 4 hours = $$\dfrac{4}{12} = \dfrac{1}{3}$$

Remaing part the cistern  =$$ 1- \dfrac{1}{3} = \dfrac{2}{3}$$

Time taken (A+B) to fill $$\dfrac{2}{3} $$part 10 hours

To fill empty tank (A+B) take = $$10 \times \dfrac{3}{2}$$

$$\Rightarrow 15 hours $$

C can tank to fill  one hours = $$\dfrac{1}{12}- \dfrac{1}{15}$$

$$\Rightarrow \dfrac{5-4}{60}  = \dfrac{1}{60}$$

C alone fill the tank in 60 hours 

C  alone fill $$\dfrac{2}{3} $$of the cistern = $$ 60 \times \dfrac{2}{3}$$

$$\Rightarrow 40 hours $$