CBSE Class 8

NCERT Solutions for Class 8 Maths Chapter 2 Linear Equations in One Variable Ex 2.2 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 2 Linear Equations in One Variable Ex 2.2.

• Linear Equations in One Variable Class 8 Ex 2.1
• Linear Equations in One Variable Class 8 Ex 2.3
• Linear Equations in One Variable Class 8 Ex 2.4
• Linear Equations in One Variable Class 8 Ex 2.5
• Linear Equations in One Variable Class 8 Ex 2.6

NCERT Solutions for Class 8 Maths Chapter 2 Linear Equations in One Variable Ex 2.2

Question 1.
If you subtract \(\frac { 1 }{ 2 } \) from a number and multiply the result \(\frac { 1 }{ 2 } \) by you get \(\frac { 1 }{ 8 } \) What is the number ?
Solution.

Question 2.
The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth. What are the length and the breadth of the pool?
Solution.

Question 3.
The base of an isosceles triangle is \(\frac { 4 }{ 3 } \)cm. The perimeter of the triangle is \(4\frac { 2 }{ 15 } \)cm. What is the length of either of the remaining equal sides ?
Solution.

Question 4.
Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.
Solution.

Question 5.
Two numbers are in the ratio 5 :3. If they differ by 18, what are the numbers?
Solution.

Question 6.
Three consecutive integers add up to 51. What are these integers ?
Solution.

Question 7.
The sum of three consecutive multiples of 8 is 888. Find the multiples.
Solution.

Question 8.
Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74. Find these numbers.
Solution.

Question 9.
The ages of Rahul and Haroon are in the ratio 5 : 7. Four years later, the sum of their ages will be 56 years. What are their present ages ?
Solution.

Question 10.
The numbers of boys and girls in a class are in the ratio 7 : 5. The number of boys is 8 more than the number of girls. What is the total class strength ?
Solution..

Question 11.
Baichung’s father is 26 years younger than Baichung’s grandfather and 29 years older than Baichung. The sum of the ages of all the three is 135 years. What is the age of each one of them ?
Solution.

Question 12.
Fifteen years from now Ravi’s age will be four times his present age. What is Ravi’s present age ?
Solution.

Question 13.
A rational number is such that when you multiply it by \(\frac { 5 }{ 2 } \) and add \(\frac { 2 }{ 3 } \) to the product, you get\(-\frac { 7 }{ 12 } \). What is the number ?
Solution.

Question 14.
Lakshmi is a cashier in a bank. She has currency notes of denominations ₹ 100, ₹ 50 and ₹ 10, respectively. The ratio of the number of these notes is 2 : 3 : 5. The total cash with Lakshmi is ₹ 4,00,000. How many notes of each denomination does she have ?
Solution.

Question 15.
I have a total of oft 300 in coins of denomination ₹ 1, ₹ 2 and ₹ 5. The number of ₹ 2 coins is 3 times the number of ₹ 5 coins. The total number of coins is 160. How many coins of each denomination are with me ?
Solution.

Hence, I have 80, 60, and 20 coins of denomination ₹ 1, ₹ 2 and ₹ 5 respectively.

Question 16.
The organizers of an essay competition decide that a winner in the competition gets a prize of ₹ 100 and a participant who does not win gets a prize of ₹ 25. The total prize money distributed is ₹ 3,000. Find the number of winners, if the total number of participants is 63.
Solution.

We hope the NCERT Solutions for Class 8 Maths Chapter 2 Linear Equations in One Variable Ex 2.2 help you. If you have any query regarding NCERT Solutions for Class 8 Maths Chapter 2 Linear Equations in One Variable Ex 2.2, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.2 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.2.

• Rational Numbers Class 8 Ex 1.1

NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.2

Question 1.
Represent these numbers on the number line.
(i) \(\frac { 7 }{ 4 } \)
(ii) \(\frac { -5 }{ 6 } \)
Solution.
(i) \(\frac { 7 }{ 4 } \)
We make 7 markings of distance \(\frac { 1 }{ 4 } \) each on the right of 0 and starting from 0. The seventh marking represents \(\frac { 7 }{ 4 } \)

(ii) \(\frac { -5 }{ 6 } \)
We make 5 markings of distance \(\frac { 1 }{ 6 } \) each on the right of 0 and starting from 0. The seventh marking represents \(\frac { -5 }{ 6 } \)

Question 2.
Represent \(\frac { -2 }{ 11 } ,\frac { -5 }{ 11 } ,\frac { -9 }{ 11 } \) on the number line.
Solution.
We make 9 markings of distance \(\frac { 1 }{ 11 } \) each on the left of 0 and starting from 0.
The second marking represents \(-\frac { 2 }{ 11 } \) the fifth marking represents \(-\frac { 5 }{ 11 } \) and the ninth marking represents \(-\frac { 9 }{ 11 } \)

Question 3.
Write five rational numbers which are smaller than 2.
Solution.
Five rational numbers which are smaller than 2 are 1, \(\frac { 1 }{ 2 } \),0, -1, \(-\frac { 1 }{ 2 } \)

Question 4.
Find ten rational numbers between \(-\frac { 2 }{ 5 } \) and \(\frac { 1 }{ 2 } \)
Solution.

Question 5.
Find five rational numbers between:

Solution.

Question 6.
Write five rational numbers greater than -2.
Solution.
Five rational numbers greater than -2 are:
\(\frac { -3 }{ 2 } \), -1, \(\frac { -1 }{ 2 } \), 0, \(\frac { 1 }{ 2 } \)
There can be many more such rational numbers

Question 7.
Find ten rational numbers between \(\frac { 3 }{ 5 } \) and \(\frac { 3 }{ 4 } \)
Solution.

We hope the NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.2 help you. If you have any query regarding NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.2, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 8 Maths Chapter 16 Playing with Numbers Ex 16.1 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 16 Playing with Numbers Ex 16.1.

• Playing with Numbers Class 8 Ex 16.2

NCERT Solutions for Class 8 Maths Chapter 16 Playing with Numbers Ex 16.1

Question 1.
Find the values of the letters in each of the following and give reasons for the steps involved.

Solution.
1.
Here, there are two letters A and B whose values are to be found out.
Let us see the sum in unit’s column. It is A + 5 and we get 2 from this. So,

2.
Here, there are three letters A, B and C whose values are to be found out.
Let us see the sum in unit’s column. It is A + 8 and we get 3 from this. So A has to be 5

That is, A = 5, B = 4 and C = 1.

4.
Here, there are two letters A and B whose values are to be found out.

5.
Here, there are three letters A, B and C whose values are to be found out.

∴ A = 5, B = 0 and C = 1

6.
Here, there are three letters A, B and C, whose values are to be found out.

7.
Here, there are two letters A and B whose values are to be found out. We have

8.
Here, there are two letters A and B whose values are to be found out.

10.
We are to find out values of A and B

We hope the NCERT Solutions for Class 8 Maths Chapter 16 Playing with Numbers Ex 16.1 help you. If you have any query regarding NCERT Solutions for Class 8 Maths Chapter 16 Playing with Numbers Ex 16.1, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.1 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.1.

• Introduction to Graphs Class 8 Ex 15.2
• Introduction to Graphs Class 8 Ex 15.3

NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.1

Question 1.
The following graph shows the temperature of a patient in a hospital, recorded every hour.
(a) What was the patient’s temperature at 1 p.m.?
(b) When was the patient’s temperature 38.5°C?
(c) The patient’s temperature was the same two times during the period given. What were these two times?
(d) What was the temperature at 1.30 p.m.? How did you arrive at your answer?
(e) During which periods did the patient’s temperature showed an upward trend?

Solution.
(а) The patient’s temperature at 1 p.m. was 36.5°C.
(b) The patient’s temperature was 38.5°C at 10.50 a.m. and 12 noon.
(c) The two times when the patient’s temperature was the same were 1 p.m. and 2 p.m.
(d) The temperature at 1.30 p.m. was 36.5°C.
From the graph, we see that the temperature was constant from 1 p.m. to 2 p.m. Since 1.30 p.m. comes in between 1 p.m. and 2 p.m., therefore we arrived at our answer.
(e) The patient’s temperature showed an upward trend during the periods 9 a.m. to 10 a.m., 10 a.m. to 11 a.m. and 2 p.m. to 3 p.m.

Question 2.
The following line graph shows the yearly sales figures for a manufacturing company.
(a) What were the sales in
(i) 2002
(ii) 2006?

(b) What were the sales in
(i) 2003
(ii) 2005?

(c) Compute the difference between sales in 2002 and 2006.
(d) In which year was there the greatest difference between the sales as compared to its previous year?

Solution.
(а) The sales in
(i) 2002 were ₹ 4 crores and in
(ii) 2006 were ₹ 8 crores.

(b) The sales in
(i) 2003 were ₹ 7 crores and in
(ii) 2005 were ₹ 10 crores.

(c) The difference between the sales in 2002 and 2006
= ₹ 8 crores – ₹ 4 crores = ₹ 4 crores

(d) The difference between sales in 2002 and 2003
= ₹ 7 crores – ₹ 4 crores = ₹ 3 crores
The difference between sales in 2003 and 2004
= ₹ 7 crores – ₹ 6 crores = ₹ 1 crore
The difference between the sales in 2004 and 2005
= ₹ 10 crores – ₹ 6 crores = ₹ 4 crores
The difference between sales in 2005 and 2006
= ₹ 10 crores – ₹ 8 crores = ₹ 2 crores
Therefore, in year 2005 the difference between the sales as compared to its previous year was the greatest.

Question 3.
For an experiment in Botany, two different plants, plant A and plant B were grown under similar laboratory conditions. Their heights were measured at the end of each week for 3 weeks. The results are shown by the following graph.

(a) How high was Plant A after
(i) 2 weeks
(ii) 3 weeks?

(b) How high was Plant B after
(i) 2 weeks
(ii) 3 weeks?

(c) How much did Plant A grow during
(d) How much did Plant B grow from the end of the 2nd week to the end of the 3rd week?
(e) During which week did Plant A grow most?
(f) During which week did Plant B grow least?
(g) Were the two plants of the same height during any week shown here? Specify.
Solution.
(а) The Plant A
after (i) 2 weeks was 7 cm high and
after (ii) 3 weeks was 9 cm high.

(b) The Plant B
after (i) 2 weeks was 7 cm high and
after (ii) 3 weeks was 10 cm high.

(c) The Plant A grew 9 cm – 7 cm = 2 cm during the 3rd week.

(d) From the end of the 2nd week to the end of the 3rd week, Plant B grew
= 10 cm – 7 cm = 3 cm.

(e) The Plant A grew in 1st week
= 2 cm – 0 cm = 2 cm
The Plant A grew in 2nd week
= 7 cm – 2 cm = 5 cm
The Plant A grew in 3rd week
= 9 cm – 7 cm = 2 cm
Therefore, Plant A grew mostly in the second week.

(f) Plant B grew in 1st week
= 1 cm – 0 cm = 1 cm
Plant B grew in 2nd week
= 7 cm – 1 cm = 6 cm
Plant B grew in 3rd week
= 10 cm – 7 cm = 3 cm
Therefore, Plant B grew least in the first week.

(g) At the end of 2nd week, the two plants shown here were of the same height.

Question 4.
The following graph shows the temperature forecast and the actual temperature for each day of a week:

(a) On which days was the forecast temperature the same as the actual temperature?
(b) What was the maximum forecast temperature during the week?
(c) What was the minimum actual temperature during the week?
(d) On which day did the actual temperature differ the most from the forecast temperature?
Solution.
(a) The forecast temperature was the same as the actual temperature on Tuesday, Friday and Sunday.
(b) The maximum forecast temperature during the week was 35°C.
(c) The minimum actual temperature during the week was 15°C.
(d)

Therefore, the actual temperature differed the most from the forecast temperature on Thursday.

Question 5.
Use the tables below to draw linear graphs.
(a) The number of days a hill side city received snow in different years.

(b) Population (in thousands) of men and women in a village in different years.

Solution.
(a)

(b)

Question 6.
Courier-person cycles from a town to a neighboring suburban area to deliver a parcel to a merchant. His distance from the town at different times is shown by the following graph.
(a) What is the scale taken for the time axis?
(b) How much time did the person take for the travel?
(c) How far is the place of the merchant from the town?
(d) Did the person stop on his way? Explain.
(e) During which period did he ride fastest?

Solution.
(a) The scale taken for the time axis is 4 units = 1 hour.
(b) The time taken by the person for the travel 8 a.m. to 11.30 a.m. = \(3\frac { 1 }{ 2 } \) hours.
(c) The place of the merchant from the town in 22 km.
(d) Yes. This is indicated by the hori¬zontal part of the graph (10 a.m. – 10.30 a.m.)
(e) He rides fastest between 8 a.m. and 9 a.m. (As line is more steep in this period).

Question 7.
Can there be a time-temperature graph as follows ? Justify your answer.


Solution.
(i) Yes; it can be
It shows a time-temperature graph. It shows an increase in temperature with an increase in time.
(ii) Yes; it can be
It shows a time-temperature graph.
It shows a decrease in temperature with increase in time.
(iii) It cannot be a time-temperature graph because it shows infinitely many different temperatures at one particular time which is not possible.
(iv) Yes; it can be
It shows a time-temperature graph,
It shows a fixed temperature at different times.

We hope the NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.1 help you. If you have any query regarding NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.1, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.1 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.1.

• Factorisation Class 8 Ex 14.2
• Factorisation Class 8 Ex 14.3
• Factorisation Class 8 Ex 14.4

NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.1

Question 1.
Find the common factors of the given terms:

Solution.

Question 2.
Factorise the following expressions:

Solution.

Question 3.
Factorise:

Solution.

We hope the NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.1 help you. If you have any query regarding NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.1, drop a comment below and we will get back to you at the earliest.