Class 8 RD Sharma Solutions Chapter 27 Introduction to Graphs Exercise 27.2 (original) (raw)

Last Updated : 16 Sep, 2024

Exercise 27.2 from Chapter 27 "Introduction to Graphs" in RD Sharma's Class 8 mathematics textbook focuses on understanding and applying the concepts of graphs. This exercise typically covers topics such as plotting points on a coordinate plane, identifying coordinates of given points, and understanding the relationship between x and y coordinates.

**Question 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 by a graph.

**Solution:

From the question as we know that,

The number of patients - is a dependent variable.

Year - is an independent variable.

Take years on x-axis

and Number of patients on y - axis

Choose the following scale:

X - axis: 2 cm = 1 year

Y - axis: 1 cm = 10 patients

Consider that on the x-axis, origin (O) represents 2001 and on the y-axis, origin (O) represents 120,

i.e. O (2001, 120).

Now, Plot

(2002, 150),

(2003, 170),

(2004, 195),

(2005, 225),

(2006, 230).

Join these points in the following graph as shown below.

**Question 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:

From the question as we know that,

Year - is an independent variable

Quantity of rice grown is a dependent variable.

So, take

Year on X - axis

Quantity of rice grown on Y - axis

Choose following scale:

X - axis: 2 cm = 1 year

Y - axis: 1 cm = 20 quintals

Consider that the origin O represents the coordinates (1999, 160).

i.e. O (1999,160)

Now, Plot

(2000, 200),

(2001, 180),

(2002, 240),

(2003, 260),

(2004, 250),

(2005, 200),

(2006, 270).

Join these points on the following graph as shown below:

Question 3. The following table gives the information regarding the number of persons employed to a piece of work and 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:

From the question as we know that,

The number of persons - is an independent variable

Time taken - is a dependent variable.

So, take

The number of persons on the X - axis

Time taken on the Y - axis.

Choose following scale:

X - axis: 2 cm = 2 persons

Y - axis: 2 cm = 2 days

Now, plot

(2, 12),

(4, 6),

(6, 4),

(8, 3).

Join these points on the following graph as shown below:

**Question 4. The following table gives the information regarding 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 cm 2 )	**1	**4	**9	**16	**25

**Draw a graph to illustrate this information.

**Solution:

From the question as we know that,

Length of a side - is an independent variable

Area of the square - is a dependent variable.

So, take

Length of a side on the X - axis

Area of the square on the Y - axis.

Choose following scale:

X - axis: 2 cm = 1 cm

Y - axis: 1 cm = 2 cm2

Now, plot

(1, 1),

(2, 4),

(3, 9),

(4, 16),

(5, 25).

Join these points in the following graph as shown below:

**Question 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:

From the question as we know that,

Year - is an independent variable

Sales - is a dependent variable.

So, take

Year on the X - axis

Sales on the Y - axis.

Choose following scale:

X - axis: 2 cm = 1 year

Y - axis: 2 cm = 1 lakh rupees

Consider that on x-axis, origin (O) represents 1991.

Hence, the coordinates of O are (1991, 0).

Now, plot

(2000, 1.5),

(2001, 1.8),

(2002, 2.4),

(2003, 3.2),

(2004, 5.4),

(2005, 7.8)

(2006, 8.6).

Join these points on the following graph as shown below;

**Question 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 **o F)	**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 **o F)	**100	**101	**104	**103	**99	**98	**100

**Solution:

****(i)** From the question as we know that,

Time - is an independent variable

Temperature - is a dependent variable.

So, take

Time on the X - axis

Temperature on the Y - axis.

Choose following scale:

X - axis: 1 cm = 1 hour

Y - axis: 1 cm = 1°F

Consider that on the x-axis, the coordinate of origin is 6:00.

On y-axis, the coordinate of origin is 94°F.

Hence, the coordinates of 0 are (6:00, 94).

Now, plot

(7:00, 100),

(9:00, 101),

(11:00, 104)

(21:00, 98)

Join these points on the following graph as shown below:

****(ii)** From the question we know that,

Time - is an independent variable

Temperature - is a dependent variable.

So, take

Time on the X - axis

Temperature on the Y - axis.

Choose following scale:

X - axis: 2 cm = 2 hours

Y - axis: 1 cm = 1°F

Consider that on the x-axis, the coordinate of origin is 6:00.

On y-axis, the coordinate of origin is 94°F.

Thus, the coordinates of 0 are (6:00, 94).

Now, plot

(8:00, 100),

(10:00, 101),

(12:00, 104)…..

(20:00, 100).

Join these points on the graph as shown below:

**Question 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:

From the question as we know that,

Time - is an independent variable.

Speed - is a dependent variable.

So, take

Time on the X - axis

Speed on the Y - axis.

Choose following scale:

X - axis: 2 big division = 1 hour

Y - axis: 1 big division = 10 km/hr

Consider that on the x-axis, the coordinate of origin (O) is 7:00.

Thus, the coordinates of O are (7:00, 0).

Now, 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).

Join these points on the graph as shown below:

Question 8. The runs scored by a cricket team in 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:

From the question as we know that,

Over - is an independent variable.

Run is a dependent variable.

So, take

Overs on the X - axis

Runs on the Y - axis.

Choose following scale:

X - axis: 1 cm = 1 over

Y - axis: 1 cm = 2 runs

Now, plot

(I, 2),

(II, 1),

(III, 4)…

(XV, 12).

Join these points on graph as shown below:

The bar graph is:

**Question 9. The runs scored by two teams A and B in 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:

From the question as we know that,

Over - is an independent variable.

Run - is a dependent variable.

So, take

Overs on X - axis

Runs on the Y - axis.

Choose following scale:

X - axis: 1 cm = 1 over

Y - axis: 1 cm = 1 run

Now, plot

(I, 2),

(II, 1),

(III, 8)…

(X, 2) for team A

and

(I, 5),

(II, 6),

(III, 8) …..

(X, 10) for team B.

Join these points on graph as shown below:

The bar graph is:

Summary

Exercise 27.2 in RD Sharma's Class 8 textbook provides students with practice in graphing points on a coordinate plane, understanding the relationship between x and y coordinates, and applying basic concepts of analytical geometry. Through various questions, students learn to plot points, identify coordinates, and analyze the properties of points in different quadrants of the coordinate system.

Class 8 RD Sharma Solutions Chapter 27 Introduction to Graphs Exercise 27.2 (original) (raw)

**Question 1. The following table shows the number of patients discharged from a hospital with HIV diagnosis in different years:

**Question 2. The following table shows the amount of rice grown by a farmer in different years:

**Question 3. **The following table gives the information regarding the number of persons employed to a piece of work and time taken to complete the work:

**Question 4. The following table gives the information regarding length of a side of a square and its area

**Question 5. The following table shows the sales of a commodity during the years 2000 to 2006.

**Question 6. Draw the temperature-time graph in each of the following cases:

**Question 7. Draw the velocity-time graph from the following data:

**Question 8. **The runs scored by a cricket team in first 15 overs are given below:

**Draw the graph representing the above data in two different ways as a graph and as a bar chart.

**Question 9. The runs scored by two teams A and B in first 10 overs are given below:

**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.

Summary

Question 3. The following table gives the information regarding the number of persons employed to a piece of work and time taken to complete the work:

Question 8. The runs scored by a cricket team in first 15 overs are given below: