Option 3 : 1.5 hrs

Pipe A can fill the tank in \(5\frac{1}{3}\) hours = \(\frac{{16}}{3}\) hours

Pipe B can fill the tank in \(2\frac{2}{5}\) hours = \(\frac{{12}}{5}\) hours

Pipe C can empty the tank in \(6\frac{2}{3}\) hours = \(\frac{{20}}{3}\) hours

Let the capacity of the tank is (L.C.M. of \({(\frac{{16}}{3},\frac{{12}}{5}\;{\rm{and}}\frac{{20}}{3})}\) i.e., **240** litres.

⇒ In 1 hour, the part of tank is filled by pipe A = 240/(16/3) = 45 litres

⇒ In 1 hour, the part of tank is filled by pipe B = 240/(12/5) = 100 litres

⇒ In 1 hour, the part of tank is emptied by pipe C = 240/(20/3) = 36 litres

According to question,

If Pipe A and pipe C opened for the first 10 hours, then, part of the tank filled = 10(45 - 36) = 90 litres.

⇒ Remaining part of tank = (240 - 90) = 150 litres

∴ Remaining part of the tank is filled by pipe B in = 150/100 hrs = 1.5 hrs.