A rectangular ice box of total surface area of \(1000 \mathrm{~cm}^2\) initially contains 1.5 kg of ice at \(0{ }^{\circ} \mathrm{C}\). If the thickness of the walls of the box is 2 mm and the temperature outside the box is \(42^{\circ} \mathrm{C}\), then the mass of the ice remaining in the box after 160 minutes is (Thermal conductivity of the material of the box \(=10^{-2} \mathrm{Wm}^{-1} \mathrm{~K}^{-1}\) and latent heat of the fusion of ice \(=336 \times 10^3 \mathrm{Jkg}^{-1}\) )

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.