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A scale of 1 inch = 50 ft is mentioned on an old map. What is the corresponding equivalent scale?
1. 1 cm = 12 m
2. 1 cm = 10 m
3. 1 cm = 6 m
4. 1 cm = 5 m

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Correct Answer - Option 3 : 1 cm = 6 m

Concept:

Representative Fraction (R.F.):

It is a ratio or fraction, that expresses the mathematical relationship between map and land. It is the ratio of the distance between any two fixed points on map to the original distance on the land.

\(\rm{R.F. =\frac{Distance\; on\; Map}{Actual\; corresponding\; distance\; on \;ground}}\)

Let the R.F be 1:100

Scale (S): Scale for the above representative fraction would be given as 1 cm to a meter.

Let suppose the denominator increases from 100 to 1000

Scale corresponding to R.F of 1: 10000 would be given as 0.1 cm to a meter.

Calculation:

Given, scale of map

1 inch = 50 ft

So, representative fraction (R.F)

\(= \frac {1\;inch}{50\;ft}\)

\(R.F = \frac {1}{50 \times 12}\)

\(R.F = \frac 1 {600}\)

Accordingly to given options scale of map

1 cm = 6 m

than \(R.F = \frac 1 {6 \times 100}\)

\(= \frac 1 {600}\)

So, answer is 1 cm = 6 m

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