Question

A private taxi charges ₨ \[230\] for a journey of \[150km\] . How much would it travel for ₨ \[540\] ?

Answer 1

Hint: Here, in the question, we have been given that a private taxi charges ₨ \[230\] for a journey of \[150km\] and we are asked to find the distance it will travel for ₨ \[540\] . We will first calculate the distance travelled per rupee by dividing the distance given by the corresponding amount and then multiply with ₨ \[540\] to calculate the required distance.

Complete step-by-step answer:
Given Distance travelled = \[150km\]
Amount charged for the given distance = ₨ \[230\]
Therefore, distance travelled for ₨ \[1\] = \[\dfrac{{150}}{{230}}km\]
It implies, distance travelled for ₨ \[540\] = \[\dfrac{{150}}{{230}} \times 540\;km\]
= \[\dfrac{{150 \times 54}}{{23}}\]
= \[352.17\;km\]
Hence, For ₨ \[540\] , taxi would travel a distance of \[352.17\;km\] .
So, the correct answer is “ \[352.17\;km\] ”.

Note: Alternatively, we can solve this question using an unknown variable. We will first find the ratio of given amount and distance and then equate it with the ratio of amount and unknown distance. Then by simplifying, we will get the value of an unknown variable which would be the desired answer.
Let \[x\] be the distance travelled for ₨ \[540\] .
We know that there is a direct relation between fare and distance. It means fare increases when the distance increases.
Therefore, \[\dfrac{{150}}{{230}} = \dfrac{x}{{540}}\]
 \[
   \Rightarrow 150 \times 240 = 230x \\
   \Rightarrow x = \dfrac{{150 \times 230}}{{540}} \\
   \Rightarrow x = 352.17km \;
 \]