1. Initial balance condition

In a metre bridge, if the balancing length is $l$ cm from one end, then

Here the two gap resistances are $2\,\Omega$ and $3\,\Omega$.

So initially,

Solving:

So the initial balancing point is at $40$ cm.

2. After adding shunt to the $3\,\Omega$ resistor

Let the shunt resistance be $X\,\Omega$. Then the effective resistance of $3\,\Omega$ in parallel with $X\,\Omega$ is

Now the two resistances are $2\,\Omega$ and $R'$.

The balance point shifts by $22.5$ cm.

Since shunting $3\,\Omega$ makes it smaller, the ratio $\frac{2}{R'}$ increases, so the balancing length must increase from $40$ cm.

Hence new balancing length is

3. Apply metre bridge balance again

So,

Now,

Solving:

4. Final answer

The derived answer matches the stored correct answer.