Three pipes A, B and C when opened together can fill a tank in $\frac{5}{2}$ hours. Pipes B and C together take 3 hours to fill the tank while pipe A and C together take 4 hours to fill the tank. How long will the pipes A and B together take to fill the tank completely ?

$6\frac{8}{13}$ $3\frac{8}{13}$ $5\frac{8}{13}$ $4\frac{8}{13}$

$4\frac{8}{13}$

The correct answer is option (4) : $4\frac{8}{13}$