Class 8 RD Sharma Solutions – Chapter 27 Introduction to Graphs – Exercise 27.2

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 cm2)	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 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) 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: