Question

Travelling \[900km\] by rail costs \[Rs.280\]. What would be the fare for a journey of \[360km\] when a person travels by the same class?

Answer 1

Hint: We are given the fare price for \[900km\] and we need to find for \[360km\]. For that, first of all we need to find for \[1km\] and then we will find for \[360km\]. We know, if we are given the price for more than \[1km\] and we need to find for \[1km\], we need to divide the price given by the distance given and When we have the price for \[1km\] and we need to find the price for more than \[1km\], we multiply the price for \[1km\] with the distance for what we have to find the price. So, in this question, first we will find the price for \[1km\] by dividing the given price with the distance given (\[900\]) and then we will find the price for \[360km\] by multiplying it with the price we will obtain for \[1km\].

Complete step by step solution:
We have,
 Cost of \[900km\] by train \[ = Rs.280\]
So now, Cost of \[1km\] by train \[ = Rs.\dfrac{{280}}{{900}}\]
(Dividing the given price by the distance)
 \[ = Rs.\dfrac{{14}}{{45}}\] (Simplifying the above expression)
Now, we have the cost of \[1km\].
We will now find the cost of \[360km\].
 We have, Cost of \[1km\]by train \[ = Rs.\dfrac{{14}}{{45}}\]
So, Cost of \[360km\] by train \[ = Rs.\dfrac{{14}}{{45}} \times 360\]
\[ = Rs.(14 \times 8)\] (Simplifying)
\[ = Rs.112\]
\[\therefore \], The fare for a journey of \[360km\] when a person travels by the same class \[ = Rs.112\]

Note: We have to read the question very carefully and understand what we are asked to find out. In this question, we first found out for \[1km\]and then for \[360km\]. We could have directly found out for \[360km\]by dividing the price for \[900km\]by \[900\]and multiplying it with \[360\]directly. It would save time also. But going step by step reduces the possibilities of errors.