Question

The plan of a map was photo copied to a reduced size such that a line originally 100 mm, measures 90 mm. The original scale of the plan was 1:1000. The approximate revised scale is

• A. \( 1:900 \)
• B. \( 1:1111 \)
• C. \( 1:1121 \)
• D. \( 1:1221 \)

Hint:

The scale is inversely proportional to the change in length on the map. If the length decreases, the representative fraction decreases (the number after '1:' increases).

Answer 1

The Correct Option is B

The original length of the line on the map was 100 mm, and the original scale was 1:1000. This means that 1 mm on the map represented 1000 mm on the ground. The actual ground length of the line = 100 mm $\times$ 1000 = 100,000 mm. After photocopying, the length of the line on the reduced map is 90 mm. The ground length remains the same (100,000 mm). The revised scale is the ratio of the new map distance to the ground distance: Revised Scale = New map distance / Ground distance Revised Scale = 90 mm / 100,000 mm Revised Scale = 9 / 10000 Revised Scale = 1 / (10000 / 9) Revised Scale = 1 / 1111.11 The approximate revised scale is 1:1111.