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:

40 hours

A + B + C = 12 hrs, 

Lets' take total efficiency as 3,

⇒ Total capacity = 3 x 12 = 36 units,

⇒ A + B + C were opened for 4 hours and then C was closed= 3 x 4 = 12,

⇒ Remaining = 36 - 12 = 24 units,

⇒ A + B filled 24 units in 10 hrs = \(\frac{24}{10}\) = 2.4   ..(Efficiency)

⇒ A + B + C = 3  (Efficiency)

⇒ 2.4 + B = 3,

⇒ B = 0.6,

⇒ \(\frac{2}{3}\)rd of total capacity = \(\frac{2}{3}\) x 36 = 24 units,

⇒ Time required by B to fill  \(\frac{2}{3}\)rd of cistern alone = \(\frac{24}{0.6}\) = 40 hrs.