Chain Surveying MCQ with answer and solution

Concept

The scale of a map is the ratio of a distance on the map to the corresponding distance on the ground. A scale with a larger RF is considered a larger scale.

Formula

RF = (Distance on Map) / (Distance on Ground)

Step-by-step solution

1. Convert all options into Representative Fraction (RF) form with identical units. 2. Option (A): 1 cm = 50 m = 1 cm / (50 × 100 cm) = 1 / 5000 = 0.0002 3. Option (B): 1 / 42000 ≈ 0.0000238 4. Option (C): 1 / 300000 ≈ 0.00000333 5. Option (D): 1 cm = 50 km = 1 cm / (50 × 1000 × 100 cm) = 1 / 5000000 = 0.000002 6. Compare the values of RF: 1/5000 is the largest value, hence (A) is the largest scale.

Explanation

A larger scale represents a smaller area in greater detail, meaning the Representative Fraction (RF) is larger (closer to 1). To compare all options, convert them into Representative Fractions (RF). Option (A): 1 cm = 50 m = 1/5000; Option (B): 1/42000; Option (C): 1/300000; Option (D): 1 cm = 50 km = 1/5000000. Among these, 1/5000 is the largest fraction.

Why the other options are wrong

B: RF is 1/42000, which is smaller than 1/5000. C: RF is given as 1/300000, which is smaller than 1/5000. D: RF is 1/5000000, which is the smallest among all options.

Shortcut

The smaller the denominator in the Representative Fraction, the larger the scale.

Common mistake

Students often confuse 'larger scale' with 'larger physical coverage on ground', picking options representing large areas like 50 km instead of small areas.