A pipe can fill a tank in 2 hours. Because of a leak in the tank, the pipe takes 2 hours 40 minutes to fill the tank. The time the leakage takes to empty the full tank is :

8 hours

Time taken by pipe alone $=2$ hours.

Rate of pipe $=\frac{1}{2}$ tank per hour.

With leakage, time taken $=2$ hours $40$ minutes $=\frac{8}{3}$ hours.

Net rate with leakage $=\frac{1}{\frac{8}{3}}=\frac{3}{8}$ tank per hour.

Leakage rate $=$ pipe rate $-$ net rate

$=\frac{1}{2}-\frac{3}{8}=\frac{4-3}{8}=\frac{1}{8}$ tank per hour.

Time taken by leakage to empty full tank:

$=\frac{1}{\frac{1}{8}}=8$ hours.

final answer: $8$ hours