Question

The scale of a map is 1:4000000. What is the actual distance between towns, if they are 5cm apart on the map.

Answer 1

Hint:
 If the distance on the map is 1 cm, the actual distance is 4000000 cm. we have to find the distance between towns if they are 5cm apart. To find the actual distance, multiply 5 with 4000000 cm. The answer will be in cm and can be converted to m or km using the formulas, 1m=100cm and 1km=1000m.

Complete step by step solution:
Given, the scale of the map as 1:4000000.
The given scale of the map can be interpreted as, if the distance on the map is 1 cm, the actual distance is 4000000 cm.
We have to find the distance between the towns that are 5 cm apart on the map.
We will multiply 5 with 4000000 to calculate the actual distance.
On, multiplying 5 with 4000000, we get the actual distance as,
\[5 \times 4000000 = 8,00,00,000{\text{ cm}}\]
As we know, that 100 cm makes 1m, divide the distance by 100 to convert the unit into metres.
 \[\dfrac{{8,00,00,000}}{{100}}{\text{ m = }}8,00,000{\text{ m}}\]
Also, 1000 m makes 1 km, divide the distance by 1000 to convert the unit into kilometres.
\[\dfrac{{8,00,000}}{{1000}}{\text{ km = }}800{\text{ km}}\]

Hence, the actual distance between the two towns is 800 km.

Note:
Units play an important role in this question. Convert the units accordingly. When we change from cm to m, we have to divide the expression by 100 and similarly when we change from m to km we have to divide the expression by 1000. Many students make mistakes in the conversion of units.