Question

Pipe A can fill a tank in 12 hours and pipe B can fill it in 15 hours seperately. A third pipe C can empty in 20 hours, Intially pipe A was opened, after one hour pipe B was opened and then after 1 hour when pipe B, was opened pipe C was also opened. In how many total hours the tank will be full?

• A. $9\frac{2}{3}$ hours
  
• B. $6\frac{2}{3}$ hours
  
• C. 10 hours
• D. none of these

Answer 1

The correct option is A $9\frac{2}{3}$ hours


Efficiency of pipe A = 8.33%

Efficiency of pipe B = 6.67%

Efficiency of pipe C = 5%

When tap C was opened,pipe A had filled 16.66% capacity

When tap C was opened,pipe B had filled 6.67% capacity

Therefore rest capacity of the tank to be filled = 100 - 23.34 = 76.66%

Now, the net efficiency of A, B and C = 10%

Hence, pipes A, B and C will take = $\frac{76.66}{10}$ = 7.66 = $7\frac{2}{3}$

Total time = 2hours + $7\frac{2}{3}$ hours = $9\frac{2}{3}$ hours.