Pipe A and Pipe B can fill the tank in 24 and 30 hrs respectively, while Pipe C can empty it in x hours. If A and B are opened for 10 hours after that C is opened, it empties the tank in 90 hours, then what is the value of x ?

Pipe A is filling the tank in 24 hours 

Pipe B is filling the tank in 30 hours

Let the total work be 120 units (LCM of 24 and 30)

Efficiency of A = $$\frac{120}{24}=5$$

Efficiency of B = $$\frac{120}{30}=4$$

Total work done by A and B together = $$\left(5+4\right)\times\ 10=90\ units$$

Pipe C can empty the tank in x hours

Given condition : 

After 10 hours C also opens and by working together it empty the tank in 90 hours 

Efficiency of C should be -10 so that , sum of efficiency of A + B + C = -1, only thatswhy tank can be empty in 90 hours

as we know, 

Work = efficiency $$\times\ $$ time 

Time taken by C = $$\frac{120}{10}=12\ hours$$

So, Pipe C can empty the tank in 10 hours

Hence, Option A is correct.