Question

On a map, a distance of 5 cm represents the actual distance of 15 Km. What is the ratio of the scale of the map?

Answer 1

Hint: Imagine the structure of your house and then think of how you can represent it on a piece of graph paper. Obviously, you will have to represent larger distances into a small space which means that you will take the ratio and then scale down the size as per the ratio. Now look at the question and think of how much you will have to enlarge 5 cm so that it can represent 15 Km.

Complete step by step solution:
Here, in this question, we will talk about the scale of a map. Now imagine, we are making a map of the country and just consider how many sheets of papers will be needed to cover the country. It is a very huge number, right? But still we see maps drawn on the papers of the size of your normal pages. How do they do it?
We will not be talking about free hand maps which don’t follow any scale but about authentic maps which can be used to even measure distances. This is done by scaling. Observe that in any standard map, on the bottom right corner, there is a scale given which shows that one centimetre is how many metres or kilometres. That is nothing but the ratio between the same.
In the question above, we have 5 cm as the representation of 15 Km and so 1 cm will represent 3 Km. as such, the accepted notation is scale: 1cm:3Km.
In standard notations though, we need ratios in same units and as such, $1Km = {10^5}cm$ and so $3Km = 3 \times {10^5}cm$ and the scale will be 1:$3 \times {10^5}$.

Note:
The scale is not always diminishing and can sometimes be enlarging when graphing out very small objects and what happens then is that the actual distance between two points is less than the distance shown and so the distance should be minimised by the scale in these cases.