Rs Aggarwal 2018 for Class 8 Math Chapter 1 - Rational Numbers

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Rs Aggarwal 2018 Solutions for Class 8 Math Chapter 1 Rational Numbers are provided here with simple step-by-step explanations. These solutions for Rational Numbers are extremely popular among Class 8 students for Math Rational Numbers Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2018 Book of Class 8 Math Chapter 1 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2018 Solutions. All Rs Aggarwal 2018 Solutions for class Class 8 Math are prepared by experts and are 100% accurate.

Page No 274:

Question 1:

The monthly income of family is ₹ 28800. The monthly expenditure of the family on various items is given below.

Item	Rent	Food	Clothing	Education	Saving
Expenditure (in ₹)	8000	10800	5600	3600	800

Represent the above data by a pie chart.

Answer:

Monthly income of the family = ₹28,800

$Central angle for each item = (\frac{Expenditure per month on various items}{Monthly income} \times 360) °$

Calculation of central angles

Items	Expenditure(in ₹)	Central angle
Rent	8000	100º
Food	10800	135º
Clothing	5600	70º
Education	3600	45º
Savings	800	10º

Construction of pie chart
Steps of construction
1. Draw a circle of any convenient radius.
2. Draw a horizontal radius of this circle.
3. Draw sectors whose central angles are 100º, 135º, 70º, 45º and 10º.
4. Shade the sectors so obtained differently and label each one of them.
Thus, the pie chart is obtained as follows.

Page No 275:

Question 2:

There are 900 creatures in a zoo as per list given below:

Beast animals	Other land animals	Birds	Water animals	Reptiles
150	400	175	125	50

Represent the above data by a pie chart.

Answer:

$Total number of creatures = 900 Central angle of each component = (\frac{number of creatures in each type}{total number of creatures} \times 360) ° Calculation of central angles$

Creatures	Number of creatures	Central angle
Beast animals	150	$60 °$
Other land animals	400	$160 °$
Birds	175	$70 °$
Water animals	125	$50 °$
Reptiles	50	$20 °$

Construction of pie chart Steps of construction : 1 . Draw a circle of any convenient radius . 2 . Draw a horizontal radius of this circle . 3 . Draw sectors whose central angles are 60 °, 160 °, 70 °, 50 ° and 20 ° . 4 . Shade the sectors so obtained differently and label each one of them . Thus, we obtain the required pie chart as shown in the figure below .

Page No 275:

Question 3:

Various modes of transport used by 1260 students in a given school are given below:

School bus	Private bus	Bicycle	Rickshaw	On foot
350	245	210	175	280

Represent the above data by a pie chart.

Answer:

$Total number of students = 1260 Central angle of each component = (\frac{number of students using that mode}{total number of students} \times 360) ° Calculation of central angles$

Mode of transport	Number of students	Central angle
School bus	350	$100 °$
Private bus	245	$70 °$
Bicycle	210	$60 °$
Rickshaw	175	$50 °$
On foot	280	$80 °$

Construction of pie chart Steps of construction : 1 . Draw a circle of any convenient radius . 2 . Draw a horizontal radius of this circle . 3 . Draw sectors whose central angles are 100 °, 70 °, 60 °, 50 ° and 80 ° . 4 . Shade the sectors so obtained differently and label each one of them . Thus, we obtain the required pie chart as shown in the figure below .

Page No 275:

Question 4:

The data given below shows number of hours spent by a school boy on different activities on a working day.

Activity	School	Homework	Play	Sleep	Others	Total
Number of hours	7	4	2	8	3	24

Represent the above data by a pie chart.

Answer:

$Total number of hours = 24 Central angle of each component = (\frac{number of hours spent on each activity}{total number of hours} \times 360) ° Calculation of central angles$

Activity	Number of hours	Central angle
School	7	$105 °$
Home work	4	$60 °$
Play	2	$30 °$
Sleep	8	$120 °$
Others	3	$45 °$

Construction of pie chart Steps of construction : 1 . Draw a circle of any convenient radius . 2 . Draw a horizontal radius of this circle . 3 . Draw sectors whose central angles are 105 °, 60 °, 30 °, 120 ° and 45 ° . 4 . Shade the sectors so obtained differently and label each one of them . Thus, we obtain the required pie chart as shown in the figure below .

Page No 275:

Question 5:

The data on religion wise division of 1080 workers of a factory are given below:

Religion	Hindu	Muslim	Sikh	Christian
Number of workers	450	270	255	105

Draw a pie chart to represent the above data.

Answer:

$Total number of workers = 1080 Central angle of each religion = (\frac{number of workers in each religion}{total number of workers} \times 360) ° Calculation of central angles$

Religion	Marks obtained	Central angle
Hindu	450	$150 °$
Muslim	270	$90 °$
Sikh	255	$85 °$
Christian	105	$35 °$

Construction of pie chart Steps of construction : 1 . Draw a circle of any convenient radius . 2 . Draw a horizontal radius of this circle . 3 . Draw sectors whose central angles are 150 °, 90 °, 85 ° and 35 ° . 4 . Shade the sectors so obtained differently and label each one of them . Thus, we obtain the required pie chart as shown in the figure below .

Page No 275:

Question 6:

The marks obtained by Sudhir in an examination are given below:

Subject	English	Hindi	Mathematics	Science	Social science
Marks obtained	105	75	150	120	90

Represent the above data by a pie chart.

Answer:

$Total marks obtained = (105 + 75 + 150 + 120 + 90) = 540 Central angle of each subject = (\frac{marks obtained in each subject}{total marks obtained} \times 360) ° Calculation of central angles$

Subject	Marks obtained	Central angle
English	105	$70 °$
Hindi	75	$50 °$
Mathematics	150	$100 °$
Science	120	$80 °$
Social science	90	$60 °$

Construction of pie chart Steps of construction : 1 . Draw a circle of any convenient radius . 2 . Draw a horizontal radius of this circle . 3 . Draw sectors whose central angles are 70 °, 50 °, 100 °, 80 ° and 60 ° . 4 . Shade the sectors so obtained differently and label each one of them . Thus, we obtain the required pie chart as shown in the figure below .

Page No 275:

Question 7:

The following table gives the number of different fruits kept in a hamper.

Type of fruit	Mangoes	Apples	Oranges	Coconuts	Pomegranates
Number	26	30	21	5	8

Represent the above data by a pie chart.

Answer:

$Total number of fruits = (26 + 30 + 21 + 5 + 8) = 90 Central angle of each fruit = (\frac{number of each type of fruit}{total number of fruits} \times 360) ° Calculation of central angles$

Types of fruit	Number	Central angle
Mangoes	26	$104 °$
Apples	30	$120 °$
Oranges	21	$84 °$
Coconuts	5	$20 °$
Pomegranates	8	$32 °$

Construction of pie chart Steps of construction : 1 . Draw a circle of any convenient radius . 2 . Draw a horizontal radius of the circle . 3 . Draw sectors whose central angles are 104 °, 120 °, 84 °, 20 ° and 32 ° . 4 . Shade the sectors so obtained differently and label each one of them . Thus, we obtain the required pie chart as shown in the figure below .

Page No 275:

Question 8:

The following data shows the agricultural production in India during a certain year.

Foodgrain	Rice	Wheat	Coarse cereals	Pulses
Production (in millions of tonnes)	57	76	38	19

Draw a pie chart to represent the above data.

Answer:

$Total production = (57 + 76 + 38 + 19) = 190 Central angle of each foodgrain = (\frac{production of each foodgrain}{total production} \times 360) ° Calculation of central angles$

Food grain	production (in millions of tonnes)	Central angle
Rice	57	$108 °$
Wheat	76	$144 °$
Coarse cereals	38	$72 °$
Pulses	19	$36 °$

Construction of pie chart Steps of construction : 1 . Draw a circle of any convenient radius . 2 . Draw a horizontal radius of the circle . 3 . Draw sectors whose central angles are 108 °, 144 °, 72 ° and 36 ° . 4 . Shade the sectors so obtained differently and label each one of them . Thus, we obtain the required pie chart as shown in the figure below .

Page No 276:

Question 9:

Given below is the result of an annual examination of a class, showing the percentage of students in each category.

First division	Second division	Third division	Failed
25%	45%	20%	10%

Represent the above data by a pie chart.

Answer:

$Total percentage = 100 Central angle of each category = (\frac{value (in %) of each category}{100} \times 360) ° Calculation of central angles$

Category	Result (in %)	Central angle
First division	25	$90 °$
Second division	45	$162 °$
Third division	20	$72 °$
Failed	10	$36 °$

Construction of pie chart Steps of construction : 1 . Draw a circle of any convenient radius . 2 . Draw a horizontal radius of the circle . 3 . Starting from the horizontal radius, draw sectors whose central angles are 90 °, 162 °, 72 ° and 36 ° . 4 . Shade the sectors so obtained differently and label each one of them . Thus, we obtain the required pie chart as shown in the figure below .

Page No 276:

Question 10:

The following table shows the percentages of buyers of four different brands of bathing soaps.

Brand	A	B	C	D
Percentage of buyers	20%	40%	25%	15%

Represent the above data by a pie chart.

Answer:

$Total percentage = 100 Central angle of each brand = (\frac{value (in %) of each brand}{100} \times 360) ° Calculation of central angles :$

Brand	Buyers (in %)	Central angle
A	20	$72 °$
B	40	$144 °$
C	25	$90 °$
D	15	$54 °$

Construction of pie chart Steps of construction : 1 . Draw a circle of any convenient radius . 2 . Draw a horizontal radius of th e circle . 3 . Draw sectors whose central angles are 72 °, 144 °, 90 ° and 54 ° . 4 . Shade the sectors so obtained differently and label each one of them . Thus, we obtain the required pie chart as shown in the figure below .

Page No 276:

Question 1:

Tick (✓) the correct answer:
A man's monthly salary is Rs 2400 and his monthly expenses on travel are Rs 250. The central angle of the sector representing travel expenses in the pie chart would be
(a) 30°
(b) $37 \frac{1}{2} °$
(c) 45°
(d) 60°

Answer:

(b) $37 \frac{1}{2} °$
$Central angle of the sector representing travel expenses = (\frac{value of expenses on travel}{monthly income} \times 360) °$
$= (\frac{250}{2400} \times 360) ° = 37 \frac{1}{2} °$

Page No 276:

Question 2:

Tick (✓) the correct answer:
If 35% of the people residing in a locality are Sikhs then the central angle of the sector representing the Sikh community in the pie chart would be
(a) 108°
(b) 115°
(c) 126°
(d) 135°

Answer:

(c) 126°
$Central angle of the sector representing the sikh community = (\frac{value (in %) of the sikh community}{100} \times 360) °$
$= (\frac{35}{100} \times 360) ° = 126 °$

Page No 276:

Question 3:

Tick (✓) the correct answer:
If in the pie chart representing the number of students opting for different streams of study out of a total strength of 1650 students, the central angle of the sector representing arts students is 48° then what is the number of students who opted for arts stream?
(a) 220
(b) 240
(c) 275
(d) 320

Answer:

(a) 220

$Let the required number of students be x . Then we have : (\frac{x}{1650} \times 360) = 48 \Rightarrow \frac{360 x}{1650} = 48 \Rightarrow x = (48 \times \frac{1650}{360}) \Rightarrow x = 220 Hence, the number of students who opted for arts stream is 220 .$

Page No 276:

Question 4:

Tick (✓) the correct answer:
In the pie chart representing the percentages of students having interest in reading various kinds of books, the central angle of the sector representing students reading novels is 81°. What is the percentage of students interested in reading novels?
(a) 15%
(b) 18%
(c) $22 \frac{1}{2} %$
(d) $27 \frac{1}{2} %$

Answer:

(c) $22 \frac{1}{2} %$

$Let the required percentage be x . Then we have : (\frac{x}{100} \times 360) = 81 \Rightarrow \frac{360 x}{100} = 81 \Rightarrow x = (81 \times \frac{100}{360}) \Rightarrow x = \frac{45}{2} \Rightarrow x = 22 \frac{1}{2} Hence, the percentage of students who are interested in reading novels is 22 \frac{1}{2} % .$

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