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:
Answer & explanation
Correct answer: option 3
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.