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Q.

Rashmi has a road map with a scale of 1 cm representing 18 km. She drives on a road for 72 km. ____ cm would be her distance covered in the map.

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Detailed Solution

Rashmi has a road map with a scale of 1 cm representing 18 km. She drives on a road for 72 km. 4 cm would be her distance covered in the map.
Given that,
A road map with a scale of 1 cm represents 18 km and Rashmi drives on a road for 72 km.
We know that if two quantities

x

and

y

vary in the same way while maintaining a constant ratio between their respective values, then the two quantities are said to be in direct proportion.
i.e.

x y = k,

where k is a constant positive number.
Here, if the scale length increases, then the representation will also increase.
So, it is a case of direct proportion.
Let us draw a table:

Distance in map cm $(x)$	$x 1 = 1$	$x 2 =$ ?
Actual distance in km $(y)$	$y 1 = 18$	$y 2 = 72$

Using the relation of direct proportion

x 1 y 1 = x 2 y 2

, we get,

x 1 y 1 = x 2 y 2

⇒ x 2 = x 1 y 2 y 1

⇒ x 2 = 1 × 72 18

∴ x 2 = 4 c m

Therefore, distance covered in map is

4 c m

.

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