Pipe A can fill an empty tank in 30 hours and B can fill it in 10 hours. Due to a leakage in the tank, it takes pipes A and B together 1.5 hours more to fill it completely that it would have otherwise taken. What is the time taken by the leakage alone to empty the same tank completely, starting when the tank is completely full?

Let's assume the total capacity of the tank is 30 units.

Pipe A can fill an empty tank in 30 hours and B can fill it in 10 hours.

Efficiency of pipe A = $$\frac{30}{30}$$ = 1 units/hour

Efficiency of pipe B = $$\frac{30}{10}$$ = 3 units/hour

Time taken by pipe A and B together to fill the tank completely = $$\frac{30}{1+3}$$

= $$\frac{30}{4}$$

= 7.5 hours

Due to a leakage in the tank, it takes pipes A and B together 1.5 hours more to fill it completely that it would have otherwise taken.

Let's assume the efficiency of leakage is 'y' units/hour.

(1+3-y)(7.5+1.5) = 30

9(4-y) = 30

3(4-y) = 10

12-3y = 10

3y = 12-10

y = $$\frac{2}{3}$$

So the time taken by the leakage alone to empty the same tank completely, starting when the tank is completely full = $$\frac{30}{\frac{2}{3}}$$

= $$\frac{30\times\ 3}{2}$$

= $$\frac{90}{2}$$

= 45 hours