Rs Aggarwal 2017 for Class 8 Math Chapter 1

Question 1:

The marks of a student in different subjects are given below:

Subject	English	Hindi	Mathematics	Science	Social science
Marks	72	63	80	56	65

Draw a bar graph from the above information.

Answer:

The following steps are followed while drawing the bar graph:

Step 1: On a graph paper, draw a horizontal line OX and a vertical line OY, representing the x-axis and y-axis, respectively.
Step 2: Along OX, write the names of the subjects at points taken at uniform gaps.
Step 3: Choose the scale: 1 small division = 1 mark
Step 4: Then the height of the various bars are:
Hindi = 72
English = 63
            Mathematics = 80
            Science = 56
            Social science = 65
Step 5: On the x-axis, draw bars of equal width and of heights obtained in step 4 at the points marked in step 2.

The completed bar graph is as shown below:

Question 2:

The following table shows the yearwise strength of a school

Year	2010−11	2011−12	2012−13	2013−14	2014−15
No. of students	950	1125	1400	1750	1900

Represent the above data by a bar graph.

Answer:

The following steps are followed while drawing the bar graph:

Step 1: On a graph paper, draw a horizontal line OX and a vertical line OY, representing the x-axis and y-axis, respectively.
Step 2: Along OX, write the time intervals in years at points taken at uniform gaps.
Step 3: Choose the scale: 1 small division = 50 students
Step 4: Then the height of the various bars are:
$Number of students in the year 2010 - 11 = (\frac{1}{50} \times 950) = 19 small divisions Number of students in the year 2011 - 12 = (\frac{1}{50} \times 1125) = 22.5 small divisions Number of students in the year 2012 - 13 = (\frac{1}{50} \times 1400) = 28 small divisions Number of students in the year 2013 - 14 = (\frac{1}{50} \times 1750) = 35 small divisions Number of students in the year 2014 - 15 = (\frac{1}{50} \times 1900) = 38 small divisions$

Step 5: On the x-axis, draw bars of equal width and of heights obtained in step 4 at the points marked in step 2.

The completed bar graph is as shown below:

Question 3:

The following table shows the favourite sports of 300 students of a school.

Sports	Cricket	Badminton	Football	Tennis	Swimming
No. of students	85	60	55	35	65

Represent the above data by a bar graph.

Answer:

The following steps are followed while drawing the bar graph:

Step 1: On a graph paper, draw a horizontal line OX and a vertical line OY, representing the x-axis and y-axis, respectively.
Step 2: Along OX, write the names of the sports at points taken at uniform gaps.
Step 3: Choose the scale: 1 small division = 1 students
Step 4: Then the height of the various bars are:
Cricket = 85
Football = 60
            Tennis = 55
            Badminton = 35
            Swimming = 65
Step 5: On the x-axis, draw bars of equal width and of heights obtained in step 4 at the points marked in step 2.
The completed bar graph is as shown below:

Question 4:

The air distances of four cities from Delhi (in km) are given below:

City	Mumbai	Kolkata	Hyderabad	Chennai
Distance from Delhi(in km)	1100	1340	1220	1700

Draw a bar graph to represent the above data.

Answer:

The following steps are followed while drawing the bar graph:

Step 1: On a graph paper, draw a horizontal line OX and a vertical line OY, representing the x-axis and y-axis, respectively.
Step 2: Along OX, write the time interval in years at points taken at uniform gaps.
Step 3: Choose the scale: 1 small division = 10 km
Step 4: Then the height of the various bars are:
$Distance of Mumbai from Delhi = (\frac{1}{10} \times 1100) = 110 small divisions Distance of Kolkata from Delhi = (\frac{1}{10} \times 1340) = 134 small divisions Distance of Hyderabad from Delhi = (\frac{1}{10} \times 1220) = 122 small divisions Distance of Chennai from Delhi = (\frac{1}{10} \times 1700) = 170 small divisions$
Step 5: On the x-axis, draw bars of equal width and of heights obtained in step 4 at the points marked in step 2.

The completed bar graph is as shown below:

Question 5:

The following table shows the life expectancy (average age to which people live) in various
countries in a particular year.

Country	India	Japan	Britain	Ethiopia	Cambodia
Lifeexpectancy (in years)	65	80	75	50	45

Represent the above data by a bar graph.

Answer:

The following steps are followed while drawing the bar graph:

Step 1: On a graph paper, draw a horizontal line OX and a vertical line OY, representing the x-axis and y-axis respectively.
Step 2: Along OX, write the names of the countries at points taken at uniform gaps.
Step 3: Choose the scale: 1 small division = 1 year
Step 4: Then the height of the various bars are:
India        : 65
Japan       : 80
            Britain    : 75
            Ethiopia : 50
            Cambodia : 45
Step 5: On the x-axis, draw bars of equal width and of heights obtained in step 4 at the points marked in step 2.
The completed bar graph is as shown below:

Question 6:

Various modes of transport used by 2150 students of a school are given below:

School bus	Private bus	Scooter	Bicycle	By foot
750	460	130	370	440

Draw a bar graph to represent the above data.

Answer:

The following steps are followed while drawing the bar graph:

Step 1: On a graph paper, draw a horizontal line OX and a vertical line OY, representing the x-axis and y-axis, respectively.
Step 2: Along OX, write the names of the states of India at points taken at uniform gaps.
Step 3: Choose the scale: 1 small division = 10 student
Step 4: Then the height of the various bars are:
$Number of students who used School bus = (\frac{1}{10} \times 750) = 75 small divisions Number of students who used Private bus = (\frac{1}{10} \times 460) = 46 small divisions Number of students who used Scooter = (\frac{1}{10} \times 130) = 13 small divisions Number of students who used Bicycle = (\frac{1}{10} \times 370) = 37 small divisions Number of students who went on their foot = (\frac{1}{10} \times 440) = 44 small divisions$
Step 5: On the x-axis, draw bars of equal width and of heights obtained in step 4 at the points marked in step 2.

The completed bar graph is as shown below:

Question 7:

The following table shows the number of motorcycles produced by a company during six
consecutive years.

2009	2010	2011	2012	2013	2014
14000	16000	18500	21000	24000	30000

Draw a bar graph to represent the above data

Answer:

The following steps are followed while drawing the bar graph:

Step 1: On a graph paper, draw a horizontal line OX and a vertical line OY, representing the x-axis and y-axis, respectively.
Step 2: Along OX, write the years of census at points taken at uniform gaps.
Step 3: Choose the scale: 1 small division = 500 motorcycles
Step 4: Then the height of the various bars are:
$Number of motorcycles in 2009 = (\frac{1}{500} \times 14000) = 28 small divisions Number of motorcycles in 2010 = (\frac{1}{500} \times 16000) = 32 small divisions Number of motorcycles in 2011 = (\frac{1}{500} \times 18500) = 37 small divisions Number of motorcycles in 2012 = (\frac{1}{500} \times 21000) = 42 small divisions Number of motorcycles in 2013 = (\frac{1}{500} \times 24000) = 48 small divisions Number of motorcycles in 2014 = (\frac{1}{500} \times 30000) = 60 small divisions$
Step 5: On the x-axis, draw bars of equal width and of heights obtained in step 4 at the points marked in step 2.

The completed bar graph is as shown below:

Question 8:

The present population (in lakhs) of six Indian states is given below:

State	Population(in lakhs)
Bihar	1040
Chhattisgarh	260
Jharkhand	330
Madhya Pradesh	720
West Bengal	910
Rajasthan	690

Represent the above data by a bar graph.

Answer:

The following steps are followed while drawing the bar graph:

Step 1: On a graph paper, draw a horizontal line OX and a vertical line OY, representing the x-axis and y-axis, respectively.
Step 2: Along OX, write the years at points taken at uniform gaps.
Step 3: Choose the scale: 1 small division = 10 lakhs
Step 4: Then the height of the various bars are:
$Population of Bihar = (\frac{1}{10} \times 1040) = 104 small divisions Population of Chhattisgarh = (\frac{1}{10} \times 260) = 26 small divisions Population of Jharkhand = (\frac{1}{10} \times 330) = 33 small divisions Population of Madhya Pradesh = (\frac{1}{10} \times 720) = 72 small divisions Population of West Bengal = (\frac{1}{10} \times 910) = 91 small divisions Population of Rajasthan = (\frac{1}{10} \times 690) = 69 small divisions$
Step 5: On the x-axis, draw bars of equal width and of heights obtained in step 4 at the points marked in step 2.

The completed bar graph is as shown below:

Question 9:

There are 1120 creatures in a zoo as per list given below:

Beast animals	Other land animals	Water animals	Birds	Reptiles
220	410	165	190	135

Represent the above data by a bar graph.

Answer:

The following steps are followed while drawing the bar graph:

Step 1: On a graph paper, draw a horizontal line OX and a vertical line OY, representing the x-axis and y-axis, respectively.
Step 2: Along OX, write the names of the places at points taken at uniform gaps.
Step 3: Choose the scale: 1 small division = 10 animals
Step 4: Then the height of the various bars are:
$Beast animals in zoo = (\frac{1}{10} \times 220) = 22 small divisions Other land animals in zoo = (\frac{1}{10} \times 410) = 41 small divisions Water animals in zoo = (\frac{1}{10} \times 165) = 16.5 small divisions Birds in zoo = (\frac{1}{10} \times 190) = 19 small divisions Reptiles in zoo = (\frac{1}{10} \times 135) = 13.5 small divisions$
Step 5: On the x-axis, draw bars of equal width and of heights obtained in step 4 at the points marked in step 2.

The completed bar graph is as shown below:

Question 10:

The following table shows the export earnings of India (in thousand crore rupees) during five consecutive years.

Year	2010−11	2011−12	2012−13	2013−14	2014−15
Export(in thousand crores rupees)	540	600	750	950	110

Represent the above data by a bar graph.

Answer:

The following steps are followed while drawing the bar graph:

Step 1: On a graph paper, draw a horizontal line OX and a vertical line OY, representing the x-axis and y-axis, respectively.
Step 2: Along OX, write the names of the countries at points taken at uniform gaps.
Step 3: Choose the scale: 1 small division = 10 thousand crore rupees.
Step 4: Then the height of the various bars are:
Export in 2010−11 : $\frac{540}{10} = 54 small divisions$

Export in 2011−12 : $\frac{600}{10} = 60 small divisions$
Export in 2012−13 : $\frac{750}{10} = 75 small divisions$
Export in 2013−14 : $\frac{950}{10} = 95 small divisions$
Export in 2013−15 : $\frac{1100}{10} = 110 small divisions$

Step 5: On the x-axis, draw bars of equal width and of heights obtained in step 4 at the points marked in step 2.

The completed bar graph is as shown below:

Question 11:

The following data shows India's total population (in millions) from 1961 to 201l.

Year	1961	1971	1981	1991	2001	2011
Population (in millions)	360	420	540	680	1020	1200

Represent the above data by a bar graph

Answer:

The following steps are followed while drawing the bar graph:

Step 1: On a graph paper, draw a horizontal line OX and a vertical line OY, representing the x-axis and y-axis, respectively.
Step 2: Along OX, write the names of the soap brands at points taken at uniform gaps.
Step 3: Choose the scale: 1 small division = 10 millions people
Step 4: Then the height of the various bars are:
Population in 1961 = $(\frac{1}{10} \times 360) = 36$ small divisions
Population in 1971 = $(\frac{1}{10} \times 420) = 42$ small divisions
Population in 1981 = $(\frac{1}{10} \times 540) = 54$ small divisions
Population in 1991 = $(\frac{1}{10} \times 680) = 68$ small divisions
Population in 2001= $(\frac{1}{10} \times 1020) = 102$ small divisions
Population in 2011 = $(\frac{1}{10} \times 1200) = 120$ small divisions
Step 5: On the x-axis, draw bars of equal width and of heights obtained in step 4 at the points marked in step 2.
The completed bar graph is as shown below:

Question 12:

In a survey of 100 families of a village, the number of members in each family was recorded, as shown by the bar graph given below:

Read the bar graph carefully and answer the following questions.
(I) What does the bar graph show?
(il) How many families have less than fivemembers?
(Iii) How many families have more than three members?
(iv) How many families have two children?

Answer:

(i) The given bar graph shows the number of members in 100 families of a village.

(ii) Number of families having 2 members = 5
Number of families having 3 members = 30
Number of families having 4 members = 55
∴Total number of families haing less than five members = 5 + 30 + 55 = 90

(iii) Number of families having 4 members = 55
Number of families having 5 members = 10
∴Total number of families haing more than three members = 55 + 10 = 65
(iv) Number of families having 2 children = Number of families having 4 members = 55 = (60+35+75+50+60)5 = 2805= 56

Question 13:

Look at the bar graph given below:

Read the above bar graph carefully and answer the questions given below.
(i) What does the bar graph show?
(tt) In which subject is the student very poor?
(Iii) If maximum marks in each subject be 100, what is the average of his marks?
(Iv) On the basis of marks obtained, fmd the subject in which the student has special interest.

Answer:

(i) The given bar graph shows the marks scored by a student in five different subjects in his exams.
(ii) It is clear from the graph that the bar of the minimum height corresponds to English. So, the student is poor in English.
(iii) Average marks scored by the student $= \frac{(55 + 80 + 30 + 60 + 45)}{5} = \frac{270}{5} = 54$
(iv) It is clear from the graph that the bar of the maximum height corresponds to Mmathematics. So, the student has special interest in mathematics.

Question 14:

Given below is a bar graph showing the heights of five mountain peaks.

Read the bar graph carefully and answer the following questions.
(i) Name the highest peak and mention its height.
(ii) What is the ratio between the heights of the lowest and the highest peaks?
(iii) Arrange the heights of the given peaks in an ascending order.
(iv) Which peaks differ in height by 600 metres?

Answer:

(i) It is clear from the graph that the bar of the maximum height corresponds to Mount Everest. So, the highest peak is Mount Everest.
The height of Mount Everest is 8800 m.

(ii) It is clear from the graph that the bar of the maximum height corresponds to Mount Everest. So, the highest peak is Mount Everest.
The height of Mount Everest is 8800 m.
It is clear from the graph that the bar of the minimum height corresponds to Annapurna. So, the lowest peak is Annapurna.
The height of Annapurna is 6000 m.
Required ratio = $\frac{8800}{6000} = \frac{22}{15}$ or 22 : 15

(iii) The heights of the given peaks 8800 m, 6000 m, 7500 m, 8200 m and 8000 m.
The heights of the given peaks in an ascending order is given by
6000 m, 7500 m, 8000 m, 8200 m and 8800 m.

(iv)The height of Mount Everest is 8800 m.
The height of Kanchenjunga is 8200 m.
The difference between the heights of these two peaks is 8800 − 8200 = 600 m.
The two peaks differ in height by 600 metres are Mount Everest and Kanchenjunga.

Rs Aggarwal 2017 for Class 8 Math Chapter 1 - Rational Numbers

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