Pipe P can fill 3/4 part of a tank in 15 hours, and pipe Q can fill 5/6 part of the same tank in 25 hours. Both P and Q were kept open for 2 hours, then both were closed. Pipe R alone was then opened and it emptied the water in the tank in 5 hours. Pipes P, Q and R together can fill the empty tank in:

Correct option is A

Given:

Pipe P fills 3/4 tank in 15 h

Pipe Q fills 5/6 tank in 25 h

P and Q run together for 2 hours, then closed

Pipe R alone empties the water filled by P & Q in 5 hours

Find time taken by P + Q + R together to fill the empty tank 

Formula Used: 

Total capacity = Rate × time 

Solution: 

Tank completely filled by 

P = $$15 \times \frac{ 4}{3}$$​ = 20 h

Q =  $$25 \times \frac{6}{5}$$​ = 30 h 

Total Capacity = LCM of 20 and 30 = 60 

Rate of P =$$\frac{60}{20}$$​ = 3

Rate of Q = $$\frac{60}{30}$$​ = 2

P + Q runs for 2 hours = (3+ 2) × 2 = 10

10 unit emptied by Q in 5 hourss

Rate of Q(emptying) = $$\frac{10}{5} = 2$$​  

Time taken by P + Q - R to fill whole tank;

= $$\frac{60}{3 + 2 -2} = \frac{60}{3} = 20 \ h$$​​