Question

The scale of a map is $1:500000$ What is the actual distance between the places, if they are $2.5cm$ apart on the map?

Answer 1

Hint: In order to solve this question, we will first discuss the basic working of measurements of quantities when expressed in maps and then using various units of conversions we will figure out the actual distance between the two places which are $2.5cm$ apart on the map.
Proportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other. Proportions are denoted using the symbol "::" or "=".


Complete step-by-step answer:
 According to the question, we have given that, the scale of map is used as $1:500000$ which is read as $1cm$ on the map scale represents the $500000\;cm$ in actual measurements so we have concluded that,
$1cm$ on map is equal to $500000\;cm$ in actual measurements so,
converting centimetre scale into metre and then into kilometre we use these general conversions as
$1cm = 0.01\;m$
so we get,
$ \Rightarrow 500000 = 5000\;m$
and also we know that, from metre and kilometre units
$1m = 0.001\;Km$
so we get,
$5000m = 5\;Km$
so, we conclude that, one centimetre on map scale actually representing the $5\;Km$ in actual measurements, so
as per the given information we have, two places are apart on map is $2.5cm$
so, simple multiplying this distance by $5\;Km$ we will get actual distance so,
$Dis\tan ce = 5 \times 2.4$ so we get,
$Dis\tan ce = 12\;Km$
So, the distance between two places which are $2.5cm$ apart on the map is $12\;Km$ in the actual distances.
So, the correct answer is “$12\;Km$”.

Note: It should be remembered that, basic units of conversions are used as $1m = 100cm{\kern 1pt} {\kern 1pt} $ and $1Km = 1000\;m$ and maps are generally mapped for cities, countries in order to locate the locations of different places with appropriate distance by using various suitable scales.