Two pipes P and Q can fill an empty tank in 25 hours and 20 hours respectively. Pipe R alone can empty the completely filled tank in 50 hours. Firstly both the pipes P and Q are opened and after 8 hours pipe R is also opened. What will be the total time (in hours) taken to completely fill the tank?

Let the capacity of tank = L.H.S. (25,20,50) = 100 litres

P and Q can fill an empty tank in 25 hours and 20 hours respectively, => (P+Q)'s efficiency = $$\frac{100}{25}+\frac{100}{20}=(4+5)=9$$ litres/hr

Similarly, R's efficiency = $$\frac{100}{-50}=-2$$ litres/hr

Let the total time (in hours) taken to completely fill the tank = $$t$$ hours

According to ques, P and Q first operated for $$8$$ hours and after that all of P,Q and R operated for $$(t-8)$$ hours

=> $$(9\times8)+(9-2)(t-8)=100$$

=> $$72+7t-56=100$$

=> $$7t=100-16=84$$

=> $$t=\frac{84}{7}=12$$ hours

=> Ans - (A)