Tank 'A' is two-fifths full. Pipe P can fill it in 10 minutes while pipe Q can empty it in 6 minutes. In what time will the tank get empty, if both P and Q are opened?

Tank A is two-fifths full.

Pipe $P$ can fill the tank in 10 minutes.

Pipe $Q$ can empty the tank in 6 minutes.

Both pipes are opened simultaneously 

Formula Used: 

Total work = Efficiency $$\times$$ time

Solution: 

LCM of 10 , 6 = 30 

Efficiency of pipe P = $$\frac{30}{10} = 3$$ 

Efficiency of emptying pipe Q = $$\frac{30}{6} = 5$$ 

total efficiency = 3 - 5 = 2 

so the tank will emptying ,

Tank is two fifth filled So, 

 = $$\frac{2}{5} \times 30 = 12$$ 

Time taken by pipes to empty the tank = $$\frac{12}{2} = 6 \, minutes$$ ​