Pipe P can fill 4/9 part of a tank in 28 hours and pipe Q can fill 3/5 part of the same tank in 27 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 D

​Given:

Pipe P can fill 4/9 part of the tank in 28 hours.
Pipe Q can fill 3/5 part of the tank in 27 hours.
Pipe R empties the tank in 8 hours.
We need to determine the time taken by pipes P, Q, and R together to fill the tank. 

Solution: 

P fill the tank   = 28  $$\times \frac{9}{4}$$ = 63 hours  

Q fill the tank = $$27 \times \frac{5}{3}$$ =  45 hours

Capacity of tank = LCM of 63 and 45 = 315 unit

Efficiency of Q = $$\frac{315}{63} = 5$$ unit/ hours

Efficiency of P = $$\frac{315}{45} = 7$$ unit/hours

Quantity of water they fill Both P and Q were kept open for 3 hours   = $$(5+7)\times 3$$ = 36  

Efficiency of R = $$\frac{36}{8} = \frac{9}{2}$$​  = 4.5 unit/   hours  

When the opened together effective efficiency = 5 + 7 - 4.5 = 7.5 unit/hours 

They together fill the tank  = $$\frac{315}{7.5}$$  = 42 hours ​