GATE 2023 CE (CE2) – Question 35
If the size of the ground area is 6 km × 3 km and the corresponding photo size in the aerial photograph is 30 cm × 15 cm, then the scale of the photograph is 1 : ______ (in integer).
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Correct answer: 20000
Explanation
**Photo scale** $=\dfrac{\text{photo distance}}{\text{ground distance}}$, with both in the same unit.
**Step 1: convert the ground length to cm.**
$$6\text{ km}=6\times1000\times100=600\,000\text{ cm}.$$
**Step 2: scale along the long side.**
$$\text{scale}=\frac{30\text{ cm}}{600\,000\text{ cm}}=\frac1{20\,000}.$$
**Check with the other side:** $3\text{ km}=300\,000$ cm and $300\,000/15=20\,000$. ✓
The scale is $1:\mathbf{20000}$.