Two pipes A and B can fill a tank in 60 minutes and 75 minutes respectively. There is also an outlet C. If A, B and C are opened together, the tank is full in 50 minutes. How much time will be taken by C to empty the full tank?

Let pipe C empty the full tank in x minutes. According to the question, $frac{1}{60}+frac{1}{75}-frac{1}{x}=frac{1}{50}$ $Rightarrow frac{1}{x}=frac{1}{60}+frac{1}{75}-frac{1}{50}$ $=frac{5+4-6}{300}=frac{3}{300}=frac{1}{100}$ $herefore x=100$ minutes Alternatives:

∴ Efficiency of C = (A + B + C) – (A + B)

= 6 – (5 + 4)

= – 3 (Here C empties).

∴ Time taken by pipe C to empty the tank

$=frac{ ext { Total work }}{ ext { Efficiency of } mathrm{C}}=frac{300}{3}=100$ minutes