Pipes A and B are emptying pipes and can empty a tank in 6 hours and 16 hours, respectively. C is a filling pipe. All the three pipes were opened together. They took 80 minutes to empty $$\frac{5}{18}th$$ of the tank. Pipe C alone can fill the tank in:

Let the volume of the tank be V 

speed of pipe A = $$\dfrac{V}{6}$$

speed of pipe B = $$\dfrac{V}{16}$$

let the speed of pipe C be = $$ \dfrac{V}{x}$$ (where x is the time taken by pipe C to fill the tank)

According to question $$ \dfrac {\dfrac{5}{8}V}{ \dfrac {V}{6} + \dfrac{V}{16} - \dfrac{V}{x}} = \dfrac {80}{60}$$

$$\Rightarrow \dfrac{5}{18}V \times \dfrac {48x}{V (8x + 13x -48)} = \dfrac {4}{3}$$

$$\Rightarrow \dfrac {40x}{3 \times (11x - 48)} = \dfrac {4}{3}$$

$$\Rightarrow 40x = 44x - 192 $$

$$\Rightarrow 4x= 192 $$

$$\Rightarrow x = \dfrac {192}{4}$$

$$\Rightarrow x = 48 $$ hours time taken by pipe C Ans