1. The resistance of a metallic wire is given by

$R = \rho \frac{L}{A}$

where:

• $\rho$ = resistivity of the material
• $L$ = length
• $A$ = area of cross section

Since the material is the same, $\rho$ remains constant.

2. New length:

The length is increased by $20\%$, so

$L' = 1.20L$

3. New area:

The area is reduced by $4\%$, so

$A' = 0.96A$

4. New resistance:

$R' = \rho \frac{L'}{A'} = \rho \frac{1.20L}{0.96A}$

$R' = \frac{1.20}{0.96} \rho \frac{L}{A}$

$R' = 1.25R$

5. Percentage change in resistance:

$\frac{R' - R}{R} \times 100 = \frac{1.25R - R}{R} \times 100$

$= 0.25 \times 100 = 25\%$

So, the resistance increases by $25\%$.