Exercise 27.2 mainly deals with the concept of the construction of graphs. The exercise problems are well framed to give a better understanding of the concepts related to the construction of graphs. Students can make use of RD Sharma Class 8 Solutions to build a strong grip on solving problems. Through regular practice, they can achieve their goals of scoring high marks in their exams. Students can download the PDF of RD Sharma Solutions Class 8 Maths Exercise 27.2 Chapter 27 from the links below.
RD Sharma Solutions for Class 8 Maths Exercise 27.2 Chapter 27 Introduction to Graphs
Access RD Sharma Solutions for Class 8 Maths Exercise 27.2 Chapter 27 Introduction to Graphs
1. The following table shows the number of patients discharged from a hospital with HIV diagnosis in different years:
| Years | 2002 | 2003 | 2004 | 2005 | 2006 |
| Number of Patients | 150 | 170 | 195 | 225 | 230 |
Represent the information with a graph.
Solution:
Here, we know that the year is an independent variable, and the number of patients is a dependent variable. So, let us take years on the x-axis and the number of patients on the y-axis.
Let us choose the following scale:
On the x-axis: 2 cm = 1 year
On the y-axis: 1 cm = 10 patients
Let us assume that on the x-axis, origin (O) represents 2001, and on the y-axis, origin (O) represents 120, i.e., O (2001, 120).
Now, let us plot (2002, 150), (2003, 170), (2004, 195), (2005, 225), (2006, 230). These points are joined to get the graph representing the given information, as shown in the figure below.
2. The following table shows the amount of rice grown by a farmer in different years:
| Years | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 |
| Rice grown (in quintals) | 200 | 180 | 240 | 260 | 250 | 200 | 270 |
Plot a graph to illustrate this information.
Solution:
We know that the year is an independent variable, and the quantity of rice grown is a dependent variable. So, let us take years on the x-axis and the quantity of rice grown on the y-axis.
By choosing the following scale:
On the x-axis: 2 cm = 1 year
On the y-axis: 1 cm = 20 quintals
Let us assume that the origin O represents the coordinates (1999, 160).
Now, let us plot (2000, 200), (2001, 180), (2002, 240), (2003, 260), (2004, 250),(2005, 200),(2006, 270).
These points are joined to get the graph representing the given information, as shown in the figure below.
3. The following table gives information regarding the number of persons employed for a piece of work and the time taken to complete the work:
| Number of persons | 2 | 4 | 6 | 8 |
| Time taken (in days) | 12 | 6 | 4 | 3 |
Plot the graph of this information.
Solution:
We know that the number of persons is an independent variable, and time taken is a dependent variable.
So, we take the number of persons on the x-axis and the time taken on the y-axis.
By choosing the following scale:
On the x-axis: 2 cm = 2 persons
On the y-axis: 2 cm = 2 days
Now, let us plot (2, 12), (4, 6), (6, 4), and (8, 3).
These points are joined to get the graph representing the given information, as shown in the figure below.
4. The following table gives information regarding the length of a side of a square and its area.
| Length of a side (in cm) | 1 | 2 | 3 | 4 | 5 |
| Area of square (in cm2) | 1 | 4 | 9 | 16 | 25 |
Draw a graph to illustrate this information.
Solution:
We know that the length of a side is an independent variable, and the area of the square is a dependent variable.
So, let us take the length of a side on the x-axis and the area of the square on the y-axis.
By choosing the following scale:
On the x-axis: 2 cm = 1 cm
On the y-axis: 1 cm = 2 cm2
Now, let us plot (1, 1), (2, 4), (3, 9), (4, 16), and (5, 25).
These points are joined to get the graph representing the given information, as shown in the figure below.
5. The following table shows the sales of a commodity during the years 2000 to 2006.
| Years | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 |
| Sales (in lakhs of Rs) | 1.5 | 1.8 | 2.4 | 3.2 | 5.4 | 7.8 | 8.6 |
Draw a graph of this information.
Solution:
We know that the year is an independent variable, and sales is a dependent variable. So, we take the year on the x-axis and sales on the y-axis.
By choosing the following scale:
On the x-axis: 2 cm = 1 year
On the y-axis: 2 cm = 1 lakh rupees
Assume that on the x-axis, origin (O) represents 1991.
So, the coordinates of O are (1991, 0).
Now, let us plot (2000, 1.5), (2001, 1.8), (2002, 2.4), (2003, 3.2), (2004, 5.4), (2005, 7.8) and (2006, 8.6).
These points are joined to get the graph representing the given information, as shown in the figure below.
6. Draw the temperature-time graph in each of the following cases:
(i)
| Time (in hours) | 7:00 | 9:00 | 11:00 | 13:00 | 15:00 | 17:00 | 19:00 | 21:00 |
| Temperature (in oF) | 100 | 101 | 104 | 102 | 100 | 99 | 100 | 98 |
(ii)
| Time (in hours) | 8:00 | 10:00 | 12:00 | 14:00 | 16:00 | 18:00 | 20:00 |
| Temperature (in oF) | 100 | 101 | 104 | 103 | 99 | 98 | 100 |
Solution:
(i) We know that time is an independent variable and temperature is a dependent variable. So, we take time on the x-axis and temperature on the y-axis.
Let us choose the following scale:
On the x-axis: 1 cm = 1 hour
On the y-axis: 1 cm = 1°F
Let us assume that on the x-axis, the coordinate of origin is 6:00.
On the y-axis, the coordinate of origin is 94°F.
So, the coordinates of 0 are (6:00, 94).
Now, let us plot (7:00, 100), (9:00, 101), (11:00, 104)…(21:00, 98)
These points are joined to get the graphs representing the given information, as shown in the figures below.
(ii) We know that, time is an independent variable and temperature is a dependent variable. So, we take time on the x-axis and temperature on the y-axis.
Let us choose the following scale:
On the x-axis: 2 cm = 2 hours
On the y-axis: 1 cm = 1°F
Let us assume that on the x-axis, the coordinate of origin is 6:00.
On the y-axis, the coordinate of origin is 94°F.
So, the coordinates of 0 are (6:00, 94).
Now, let us plot (8:00, 100), (10:00, 101), (12:00, 104) ….. (20:00, 100).
These points are joined to get the graphs representing the given information, as shown in the figures below.
7. Draw the velocity-time graph from the following data:
| Time (in hours) | 7:00 | 8:00 | 9:00 | 10:00 | 11:00 | 12:00 | 13:00 | 14:00 |
| Speed (in km/hr) | 30 | 45 | 60 | 50 | 70 | 50 | 40 | 45 |
Solution:
We know that, time is an independent variable and speed is a dependent variable. So, we take time on the x-axis and speed on the y-axis.
By choosing the following scale:
On the x-axis: 2 big divisions = 1 hour
On the y-axis: 1 big division = 10 km/hr
Let us assume that on the x-axis, the coordinate of origin (O) is 7:00.
So, the coordinates of O are (7:00, 0).
Now, let us plot (7:00, 30), (8:00, 45), (9:00, 60), (10:00, 50), (11:00, 70), (12:00, 50), (13:00, 40), (14:00, 45).
These points are joined to get the graph representing the given information, as shown in the figure below.
8. The runs scored by a cricket team in the first 15 overs are given below:
| Overs: | I | II | III | IV | V | VI | VII | VIII | IX | X | XI | XII | XIII | XIV | XV |
| Runs: | 2 | 1 | 4 | 2 | 6 | 8 | 10 | 21 | 5 | 8 | 3 | 2 | 6 | 8 | 12 |
Draw the graph representing the above data in two different ways as a graph and as a bar chart.
Solution:
We know that over is an independent variable and run is a dependent variable. So, we take overs on the x-axis and runs on the y-axis.
By choosing the following scale:
On the x-axis: 1 cm = 1 over
On the y-axis: 1 cm = 2 runs
Now, let us plot (I, 2), (II, 1), (III, 4)… (XV, 12).
These points are joined to get the graph representing the given information, as shown in the figure below.
The bar graph is as follows:
9. The runs scored by two teams, A and B, in the first 10 overs are given below:
| Overs | I | II | III | IV | V | VI | VII | VIII | IX | X |
| Team A | 2 | 1 | 8 | 9 | 4 | 5 | 6 | 10 | 6 | 2 |
| Team B | 5 | 6 | 2 | 10 | 5 | 6 | 3 | 4 | 8 | 10 |
Draw a graph depicting the data, making the graphs on the same axes in each case in two different ways as a graph and as a bar chart.
Solution:
We know that over is an independent variable and run is a dependent variable. So, we take overs on the x-axis and runs on the y-axis.
By choosing the following scale:
On the x-axis: 1 cm = 1 over
On the y-axis: 1 cm = 1 run
Now, let us plot (I, 2), (II, 1), (III, 8)… (X, 2) for team A and (I, 5), (II, 6), (III, 8) ….. (X, 10) for team B.
These points are joined to get the graph representing the given information, as shown in the figure below.
The bar graph is as follows:
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