Question

On a particular day the exchange rate of 1 Euro was 55 rupees. The following linear graph shows the relationship between the two currencies. Read the graph carefully and answer the following questions:
(i) Find the value of 4 Euros in rupees.
(ii) Find the value of Rs. 275 in terms of Euros.

Answer 1

Hint: For solving this problem we consider the parameter on x-axis as \['x'\] and the parameter on y-axis as \['y'\]. Here, we have two points of \[\left( {{x}_{1}},{{y}_{1}} \right),\left( {{x}_{2}},{{y}_{2}} \right)\]. So, we need to find the equation of line in two point form as \[y-{{y}_{1}}=m\left( x-{{x}_{1}} \right)\] where \['m'\] is the slope given as \[m=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\]. After we get the equation of line we can find the values of \['x'\] knowing \['y'\] and vice-versa.

Complete step-by-step solution
We are given that the exchange rate as
1 Euro is equal to 55 rupees
20 Euros is equal to 1,000 rupees.
Let us assume that the values of Euros as \['x'\] and values of rupees as \['y'\].
Here, we have two points in the graph, let us assume \[P\left( {{x}_{1}},{{y}_{1}} \right)=\left( 1,55 \right),Q\left( {{x}_{2}},{{y}_{2}} \right)=\left( 20,1000 \right)\].
Let us find the equation of line ‘PQ’ from two point form that is if \[\left( {{x}_{1}},{{y}_{1}} \right) and \left( {{x}_{2}},{{y}_{2}} \right)\] are two points, then the line equation is given as \[y-{{y}_{1}}=m\left( x-{{x}_{1}} \right)\] where \['m'\] is the slope given as \[m=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\].
By using the above equation let us find the slope by substituting the values of \[\left( {{x}_{1}},{{y}_{1}} \right) and \left( {{x}_{2}},{{y}_{2}} \right)\] in above equation we get
\[\begin{align}
  & \Rightarrow m=\dfrac{1000-55}{20-1} \\
 & \Rightarrow m=\dfrac{945}{19} \\
\end{align}\]
Now, let us find the equation of ‘PQ’ by substituting required values in \[y-{{y}_{1}}=m\left( x-{{x}_{1}} \right)\] we get
\[\begin{align}
  & \Rightarrow y-55=\dfrac{945}{19}\left( x-1 \right) \\
 & \Rightarrow 19y-1045=945x-945 \\
 & \Rightarrow 945x-19y+100=0 \\
\end{align}\]
Therefore we got the equation how the values of Euros and rupees are changing as \[945x-19y+100=0\].
Now let us solve first part
(i) We are given 4 Euros.
As we assumed that Euros as \['x'\] we can write \[x=4\].
By substituting \[x=4\] in \[945x-19y+100=0\] we get value of \['y'\] as
\[\begin{align}
  & \Rightarrow 945\left( 4 \right)-19y+100=0 \\
 & \Rightarrow 19y=3780+100 \\
 & \Rightarrow y=204.21 \\
\end{align}\]
Therefore, we can say that 4 Euros is equal to 204.21 rupees.
Now, let us solve the second part.
(ii) We are given with Rs. 275
As we assumed that Euros as \['y'\] we can write\[y=275\].
By substituting \[y=275\] in \[945x-19y+100=0\] we get value of \['x'\] as
\[\begin{align}
  & \Rightarrow 945x-19\left( 275 \right)+100=0 \\
 & \Rightarrow 945x=5225+100 \\
 & \Rightarrow x=5.63 \\
\end{align}\]
Therefore, we can say that 275 rupees is equivalent to 5.63 Euros.

Note: Students may make mistakes by solving the problem directly without finding the equation. That is we are given that 1 Euro is equal to 55 rupees then they calculate the value of 4 Euros by directly multiplying with 55 and saying 4 Euros equal to \[220\left( =4\times 55 \right)\] rupees which is the wrong answer. Here, the value of Euros to rupees is not constant, it is changing linearly. So, we need to find the equation to solve the problem.