Question & Answer

On a map, 1 centimetre represents 100,000 centimetres. What is the length of a road in kilometres that measures 2.9 centimetres on the map?
A. 29
B. 2.9
C. 2900
D. 0.29

ANSWER Verified Verified
Hint: Use unitary method to calculate the length of the road. As in the question, the length represented by 1cm in the map is given and we need to find the distance measured by 2.9cm.

Complete step-by-step solution -
According to the question, 1cm on the map represents 100,000 centimetres.
i.e. 1cm on map = 100,000 cms on road ……………(1)
And, we need to find the length of the road in kms which is represented by 2.9cm.
By unitary method;
If ‘1’ units of A = b units of B
Then, ‘K’ units of A = $\left( K\times b \right)$units of B.
Here, 1cm of map = 100,000 cm of road.
  & \Rightarrow 2.9cm\ of\ map\ =\left( 2.9\times 100,000 \right)cm\ of\ road \\
 & =290000\ cm\ of\ road \\
We have got the required length of road in cm. But according to the question, we need to find this length in kilometres.
Now, use unit conversion;
We know, 1 m = 100 cm
and 1 km = 1000 m
  & \Rightarrow 29000cm=\dfrac{290000}{100}m \\
 & =290m \\
 & =\dfrac{2900}{1000}km \\
 & =2.9km \\
Hence, the required length of road = 2.9km
So, option (B) will be the correct answer.

Note: Be careful that for converting cm into km we divide it by ${{10}^{5}}$, not multiply. Whenever we need to convert larger quantity into smaller quantity, we multiply with the conversion factor and when we need to convert the smaller quantity to larger one, divide by conversion factor.