Pipe A can fill an empty cistern in 15 hours while Pipe B takes 25 hours to fill it. Initially Pipe A is left open for some time and then closed and Pipe B is switched on immediately. In all the cistern rakes 21 hours to be filth How long was Pipe A open?

Pipe A can fill an empty cistern in 15 hours while Pipe B takes 25 hours to fill it. Initially Pipe A is left open for some time and then closed and Pipe B is switched on immediately. In all the cistern rakes 21 hours to be filled.

Time Taken    Work Done     Efficiency

A  -  15         LCM (15,25)     $$\frac{75}{15} =5$$

B  -   25             = 75             $$\frac{75}{25}=3$$

Let x be time for which Pipe A was open

So according to question,

$$A\times x +B(21-x) =75$$

$$5\times x +3(21-x) =75$$

$$2x +63 =75$$

$$2x =12$$

$$x=6$$

Option C is correct.