A pipe can fill a tank in 30 minutes. Due to two leakages A and B, the filled tank would be drained off in $$1\frac{1}{2}$$ hour and $$1\frac{1}{4}$$ hour respectively. How long will it take to fill the tank if the pipe, A and B are left open?

0.5 hour will take to full tank.

So, in 1 hour it will fill 2 times of tank.

first drain will clear $$(2/3)$$ part of the tank in 1 hour.

second drain will clear $$(4/5)$$ part of the tank in 1 hour.

So, in 1 hour ,both the tank will clear (together)$$=(2/3)+(4/5)=22/15.$$

part of the tank.

So, when these three open together,

the resultant part will fill in 1 hour 

$$=2-(22/15)=8/15.$$

So, full tank will be filled in 15/8 hours.

So, Option A is correct.