Pipe P can fill $$\frac{5}{9}$$ part of a tank in 25 hours and pipe Q can fill $$\frac{8}{9}$$ part of the same tank in 24 hours. Both P and Q were kept open for 3 hours, then both were closed. Pipe R alone was then opened and it emptied the water in the tank in 8 hours. Pipes P, Q and R together can fill the empty tank in: ​

Correct option is C

Given:

P fills $$\frac{5}{9}$$​ of tank in 25 h; Q fills $$\frac{8}{9}$$​ in 24 h

P and Q run for 3 h, then R alone empties that water in 8 h

Find time if P, Q, R run together

Solution:

P rate $$=\frac{\frac{5}{9}}{25}=\frac{1}{45}$$​ tank/h

Q rate $$=\frac{\frac{8}{9}}{24}=\frac{1}{27}$$​ tank/h

In 3 h, P + Q fill

​$$\left(\frac{1}{45}+\frac{1}{27}\right)=3\times\frac{8}{135}$$​=$$\frac{8}{45}$$​ of tank

R empties $$\frac{8}{45}$$​ in 8 h

R rate $$=\frac{\frac{8}{45}}{8}=\frac{1}{45}$$​ tank/h (emptying)

Net rate with P + Q + R:
$$\frac{1}{45}+\frac{1}{27}-\frac{1}{45}=\frac{1}{27}$$​ tank/h

Time to fill =$$\frac{1}{\frac 1{27}}= 2$$​7 hours