Question

A map is drawn on the scale of \[4{\rm{mm}}\] for each \[16{\rm{km}}\]. Two places are shown on the map at the distance of \[7.2{\rm{mm}}\] . How far away they are from each other?
A) \[22.3{\rm{km}}\]
B) \[9.21{\rm{km}}\]
C) \[28.8{\rm{km}}\]
D) \[21.8{\rm{km}}\]

Answer 1

Hint:
Here, we will use the scale on which the map is drawn. We will use the unitary method to find the distance between them. After simplifying and applying different mathematical operations, we will get the final answer.

Complete step by step solution:
It is given that the map is drawn on the scale of \[4{\rm{mm}}\] for each \[16{\rm{km}}\].
\[4{\rm{mm}}\] distance on map is equal to the distance of \[16{\rm{km}}\] on road.
Using unitary method, we get
\[1{\rm{mm}}\] distance on map \[ = \dfrac{{16{\rm{km}}}}{{4{\rm{mm}}}} \times 1{\rm{mm}} = 4{\rm{km}}\] distance on road.
It is given that the distance between the two places on the map is equal to \[7.2{\rm{mm}}\].
To calculate the actual distance, we will multiply this distance by the number 4 as \[1{\rm{mm}}\] distance on map is equal to the distance of \[4{\rm{km}}\] on the road.
Therefore, the actual distance between these two places \[ = 7.2 \times 4{\rm{km}} = 28.8{\rm{km}}\]

Hence, the correct option is option C.

Note:
Here, we have used the unitary method to solve the question. The unitary method is defined as a method in which we find the value of a unit and then the value of a required number of units. We can make a mistake by dividing \[1{\rm{mm}}\] distance on map by \[7.2{\rm{mm}}\] instead of multiplying the terms. In this question, the scale of the map is given. The scale of a map is defined as the ratio of a distance on the map to its corresponding distance on the ground or road.