Question

The scale of a map is \[1:3000000\]. What is the actual distance between the two towns if they are \[3.5{\text{ cm}}\] apart on the map?

Answer 1

Hint: We will solve this question by converting the given ratio into the actual form for example, if the scale of a map is \[1:50000\], then it means that \[1{\text{ cm}}\] on the map represents \[50000{\text{ cm}}\] or \[500{\text{ m}}\] \[{\text{0}}{\text{.5 km}}\] on the map because \[{\text{100 cm = 1 m}}\] and \[{\text{1000 m = 1 km}}\].

Complete step-by-step solution:
Step 1: It is given that the scale of a map is \[1:3000000\] which means that \[1{\text{ cm}}\] the map represents \[3000000{\text{ cm}}\] on the map.
By converting \[3000000{\text{ cm}}\] into kilometers we get:
\[3000000{\text{ cm = 30000 m}}\] and \[{\text{30000 m = 30 km}}\].
Step 2: Now, the distance between the two towns is \[3.5{\text{ cm}}\]. So we will calculate the actual distance between the two towns by multiplying the representation on a scale of a map with the distance given between them as shown below:
\[ \Rightarrow {\text{Actual distance}} = 3.5 \times 30\]
By multiplying on the RHS side of the above expression we get:
\[ \Rightarrow {\text{Actual distance}} = 105{\text{ km}}\]

The actual distance between the towns is \[105{\text{ km}}\].

Note: For solving these types of questions students should follow the below steps:
For calculating the distance, you should first need to measure the length using a ruler in any unit’s centimeters or millimeters between two points.
 Now after writing that measurement you need to check the scale of the map on which both points are found.
Now, multiply the distance found between the two points by the scale of the map.
Convert the answer into the unit of distance which is kilometers.
Remember the basic conversions for example \[{\text{100 cm = 1 m}}\] and \[{\text{1000 m = 1 km}}\].