Pipes And Cisterns Q12

12. A pipe A can fill the tank in 10 hrs, B can fill it in 20 hrs and C can empty in 40 hrs. All are  opened at the same time. After how many hours shall the pipe B be closed such that the tank can be filled in 10 hrs?

A.15 Hrs                                 B.5 Hrs

C.10 Hrs                                  D.2Hrs

Answer:

Let the pipe B be closed after x hrs.

Then A worked for 10 hrs, B worked for x hrs and C worked for 10 hrs.

mA + nB – oC = 1    (since C is outlet)

10(1/10) + x(1/20) – 10(1/40) = 1

x = 5 hrs.