Question

When Rupa was born, her father was 25 years old. Form an equation and draw a graph for this data. From the graph find
(i) The age of the father when Rupa is 25 years old.
(ii) Rupa’s age when her father is 40 years old.
(a) (i) 50 (ii) 15
(b) (i) 25 (ii) 15
(c) (i) 65 (ii) 45
(d) (i) 29 (ii) 76

Answer 1

Hint: Assume that Rupa’s age is ‘x’ and her father’s age is ‘y’. Use the fact that the difference between Rupa and her father’s age is 25 years to write the equation relating both of their ages. Plot the graph based on the equation. Plot the point on the graph at which Rupa’s age is 25 and her father’s age is 40. Check the corresponding value of other variables to find the ages.

Complete step-by-step answer:

We know that Rupa’s father was 25 years old when Rupa was born. We have to write equations relating the age of both of them.
Let’s assume that Rupa’s age is ‘x’ and her father’s age is ‘y’. We observe that the difference between their ages is 25. As Rupa’s father is older than her, we have $y-x=25$.
Thus, the equation relating both of their ages is $y=x+25$. We will now plot the equation of this line. We will find any two points on this line.
For $x=0$, we have $y=25$. Thus, we have $A=\left( 0,25 \right)$.
For $x=20$, we have $y=20+25=45$. Similarly, we have $B=\left( 20,45 \right)$.
We will now plot the points A and B on the plane and join them to plot the equation of the line $y=x+25$.

Thus, we have plotted the line $y=x+25$.
We will now use the graph to find Rupa’s and her father’s age.
(i) We know that the age of Rupa’s father is 40 years. We have to find her age.
Let’s assume her age is ‘x’.
So, the point on the line is $D=\left( x,40 \right)$.
Plotting the point on the line, we have

We observe that point C corresponds to $C=\left( 25,50 \right)$. Thus, we have $\left( 25,50 \right)=\left( 25,y \right)\Rightarrow y=50$.
Thus, the age of Rupa’s father is 50years.
(ii) We know that Rupa’s age is 25 years. We have to find her father’s age.
Let’s assume her father’s age is ‘y’.
So, the point on the line is $C=\left( 25,y \right)$.
Plotting the point on the line, we have

We observe that point D corresponds to $D=\left( 15,40 \right)$. Thus, we have $\left( 15,40 \right)=\left( x,40 \right)\Rightarrow x=15$.
Thus, Rupa’s age is 15years.
Hence, the correct answer is (i) 50 (ii) 15, which is option (a).

Note: One must keep in mind that all the ages must be in the same unit, i.e., years. We can also calculate Rupa and her father’s age by substituting the value of one variable in the equation $y=x+25$ to calculate the value of another variable. We can verify that the values calculated from the graph and using the equation are the same or not.