Two pipes A and B can fill a tank in 36 min. and 45 min. respectively. Another pipe C can empty the tank in 30 min. First A and B are opened. After 7 minutes, C is also opened. The tank filled up in:

Explanation:-

Pipe A can fill empty tank in 30 min.
Pipe A can fill the tank = $$\frac{{100}}{{36}}$$ = 2.77% per minute
Pipe B can fill empty tank in 45 min.
Pipe B can fill the tank = $$\frac{{100}}{{45}}$$ > = 2.22% per min.
A and B can together fill the tank
= (2.77 + 2.22)= 5% per minute
So, A and B can fill the tank in 7 min.
= 7 × 5 = 35% of the tank
Rest tank to be filled = 100 - 35 = 65%
C can empty the full tank in 30 min.
C can empty the tank = $$\frac{{100}}{{30}}$$ = 3.33% per min.
C is doing negative work i.e. emptying the tank
A, B and C can together fill the tank,
= 2.77% + 2.22% - 3.33% = 1.67% tank per minute
So, A, B and C will take time to fill 65% empty tank,
= $$\frac{{65}}{{1.67}}$$ = 39 min. (Approx)