Discussion
If a map is drawn on the R. F. = 1 : 50,000 but when the same map is redrawn on R.F. = 1 : 2,50,000. The status of redrawn new map is :
Answer: A
The redrawn map is reduced by 5 times.
The representative fraction compares map distance with ground distance. At 1 : 50,000, 1 cm represents 50,000 cm; at 1 : 2,50,000, 1 cm represents 2,50,000 cm. The same ground distance therefore appears on the new map at
\[ \begin{aligned} \frac{1/250000}{1/50000} &= \frac{50000}{250000} \\ &= \frac{1}{5} \end{aligned} \]
of its original length, so the map is reduced five times in linear scale (and 25 times in area). It is not enlarged, because the denominator has grown, and 2.5 is a misreading of the 2,50,000.
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