For cell of emf E balancing length
$=\frac{L}{3}=\frac{1}{3}\times L$ (length of wire)
Increased length of wire = $L+\frac{L}{2}=\frac{3L}{2}$
Since, the cell is the same, therefore the new balancing length
= $\frac{1}{3}$ (new increased length)
$=\frac{1}{3}\times \frac{3}{2}L$
$=\frac{L}{2}$
Therefore, for the same cell the balance point will be as length $\frac{L}{2}$ from positive end.