GATE Mechanical Engineering (ME) 2019 Shift 2 Solved Paper

1 hour work of P=1/6
1 hour work of Q=1/9
1 hour work of R=−1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours =4(1/6−1/12)=1/3
Tank filled by when Q and R works for another 6 hours =6(1/9−1/12)=1/6
Total tank filled in these 10 hours =1/3+1/6=0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in 9 hours)
Therefore, total time required to fill the tank =4+6+4.5=14.5 hours