Question

Namita travels 20 km 50 m every day. Out of this she travels 10 km 200 m by bus and the rest by auto. How much distance does she travel by auto?

Answer 1

Hint: This question is based on unit conversion and simple addition and subtraction. In this question Namita travels a certain distance by bus and by auto every day. We have to find the distance travelled by Namita by auto. The unit of the distance is given in mixed form, so we have to simplify the units into single unit form and then solve the question.

Complete step-by-step answer:
Given:
Let us assume the total distance travelled by Namita every day is x, the distance travelled by bus is y and the distance travelled by auto is z.
Then, we have given,
The total distance travelled
 $\Rightarrow x = 20{\text{ km 50 m}} $
Unit conversion formula used to convert kilometres into meters is-
 $ 1{\text{ km = 1000 m}} $
So, using this formula we get,
 $
\Rightarrow x = 20 \times 1000 + {\text{ 50 m}}\\
x = 20000 + 50\\
x = 20050 m\\
$
Similarly, the distance travelled by bus
 $
\Rightarrow y = {\text{10 km 200 m}}\\
\Rightarrow {\text{y = 10}} \times {\text{1000 + 200}}\\
\Rightarrow {\text{y = 10000 + 200 }}\\
\Rightarrow {\text{y = 10200 m}}
 $
And, according to the question, the total distance travelled by Namita every day is the sum of the distance travelled by bus and the distance travelled by auto.
So, we have,
$\Rightarrow x = y + z $
Substituting the values of x and y in the equation we get,
 $
\Rightarrow {\text{20050 m = 10200 m + z}}\\
\Rightarrow {\text{z = }}\left( {{\text{20050 - 10200}}} \right){\text{ m}}\\
\Rightarrow {\text{z = 9850 m}}
 $
We can write this value, by using the conversion formula in this form –
 $
\Rightarrow z = \dfrac{{9850}}{{1000}}{\text{ km}}\\
\Rightarrow {\text{z = 9}}{\text{.850 km}}
 $
Or we can say,
 $ z = {\text{ 9 km 850 m}} $

Therefore, the distance travelled by auto is 9 km 850 m.

Note: While doing the addition and subtraction the unit of the distances given should be the same, it means that if one unit of the distance is given in meters and another is given in kilometres then while addition all the units of the distances should be converted in either meters or kilometres.