Given data

• Initial temperature: $T_0 = 27^\circ\mathrm{C}$
• Resistance at $27^\circ\mathrm{C}$: $R_0 = 50\,\Omega$
• Temperature coefficient: $\alpha = 2.4 \times 10^{-4}\,^\circ\mathrm{C}^{-1}$
• Final resistance: $R = 62\,\Omega$

Use the linear relation of resistance with temperature

$R = R_0\left[1 + \alpha (T - T_0)\right]$

Substitute the values:

$62 = 50\left[1 + 2.4 \times 10^{-4}(T - 27)\right]$

Simplify the equation

Divide both sides by $50$:

$\frac{62}{50} = 1 + 2.4 \times 10^{-4}(T - 27)$

$1.24 = 1 + 2.4 \times 10^{-4}(T - 27)$

$0.24 = 2.4 \times 10^{-4}(T - 27)$

Solve for $T$

$T - 27 = \frac{0.24}{2.4 \times 10^{-4}}$

$T - 27 = 1000$

$T = 1027^\circ\mathrm{C}$

Final answer

$\boxed{1027}$

Comparison with stored answer

Stored correct answer = $1027$

This matches the derived answer.