GATE 2024 EC GA Q.10: solution and answer

Official answer: ASource: Official answer key, GATE 2024 EC (IISc Bengaluru)

1. When a sheet is folded in half along an axis parallel to one pair of edges, those edges keep their length and the side at right angles to the axis is halved.

2. FO1 folds along an axis parallel to the initial long edge ($24\text{cm}$). The $24\text{cm}$ side stays the same and the $16\text{cm}$ side is halved at each fold: $16\to 8\to 4$.

3. Sheet A after two FO1 folds measures $24\text{cm}\times 4\text{cm}$, so its perimeter is $P_A=2(24+4)=56\text{cm}$.

4. FO2 folds along an axis parallel to the initial short edge ($16\text{cm}$). The $16\text{cm}$ side stays the same and the $24\text{cm}$ side is halved at each fold: $24\to 12\to 6$. After the first fold the sheet is $12\times 16$, and the question fixes the axis by the initial short edge, so the second fold still halves the $12\text{cm}$ side.

5. Sheet B after two FO2 folds measures $6\text{cm}\times 16\text{cm}$, so its perimeter is $P_B=2(6+16)=44\text{cm}$.

6. Ratio of the perimeters: $$\frac{P_A}{P_B}=\frac{56}{44}=\frac{14}{11}$$ The answer is 14:11, option (A).