NCERT Solutions for Class 6 Maths offer comprehensive explanations for the questions found within the NCERT textbooks endorsed by the Central Board of Secondary Education (CBSE). Orchids the international school provides these NCERT Class 6 Maths Solutions on a chapterbychapter basis, aiming to assist students in resolving any uncertainties and acquiring a profound comprehension of the subject matter. These resources, including NCERT Solutions, are conveniently accessible in PDF format, allowing students to download them for offline learning.
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Catherine threw a dice 40 times and noted the number appearing each time as shown below :
1 
3 
5 
6 
6 
3 
5 
4 
1 
6 
2 
5 
3 
4 
6 
1 
5 
5 
6 
1 
1 
2 
2 
3 
5 
2 
4 
5 
5 
6 
5 
1 
6 
2 
3 
5 
2 
4 
1 
5 
Make a table and enter the data using tally marks. Find the number that appeared.
(a) The minimum number of times
(b) The maximum number of times
(c) Find those numbers that appear an equal number of times.
Numbers 
Tally Marks 
Number of times 
1 
 
7 
2 
 
6 
3 
5 

4 
 
4 
5 
 
11 
6 
 
7 
(a) The number that occurred for minimum number of times is 4
(b) The number that occurred for maximum number of times is 5
(c) 1 and 6 are the numbers that appear an equal number of times
Following pictograph shows the number of tractors in five villages.
Observe the pictograph and answer the following questions.
(i) Which village has the minimum number of tractors?
(ii) Which village has the maximum number of tractors?
(iii) How many more tractors village C has as compared to village B.
(iv) What is the total number of tractors in all the five villages?
(i) Village D has the minimum number of tractors.
(ii) Village C has the maximum number of tractors.
(iii) Village B has 5 tractors
Village C has 8 tractors
= 8 – 5
= 3 tractors
Village C has 3 more tractors as compared to village B
(iv) Total number of tractors in all the villages = 6 + 5 + 8 + 3 + 6 = 28 tractors
The number of girl students in each class of a coeducational middle school is depicted by the pictograph:
Observe this pictograph and answer the following questions:
(a) Which class has the minimum number of girl students?
(b) Is the number of girls in Class VI less than the number of girls in Class V?
(c) How many girls are there in Class VII?
By observing the above table, there are 24, 18, 20, 14, 10, 16, 12 and 6 girls respectively from class I to VIII
(a) Class VIII has only 6 girls. Therefore, the minimum number of girl students are in Class VIII
(b) No. Class V has 10 girl students
Class VI has 16 girl students
Hence, the number of girls in Class VI are more than the number of girls in Class V
(c) The number of girls in Class VII are 12
The sale of electric bulbs on different days of a week is shown below:
Observe the pictograph and answer the following questions:
(a) How many bulbs were sold on Friday?
(b) On which day were the maximum number of bulbs sold?
(c) On which of the days same number of bulbs were sold?
(d) On which of the days minimum number of bulbs were sold?
(e) If one big carton can hold 9 bulbs. How many cartons were needed in the given week?
(a) Number of bulbs sold on Friday are 14 bulbs.
(b) On Sunday highest number of bulbs i.e 18 are sold. Thus, maximum number of bulbs were sold on Sunday.
(c) On Wednesday and Saturday 8 bulbs are sold. Hence, equal number of bulbs were sold on Wednesday and Saturday.
(d) Minimum number of bulbs were sold on Wednesday and Saturday i.e., 8 bulbs.
(e) Total number of bulbs sold in a week = 12 + 16 + 8 + 10 + 14 + 8 + 18 = 86
In a village six fruit merchants sold the following number of fruit baskets in a particular season:
Observe this pictograph and answer the following questions:
(a) Which merchant sold the maximum number of baskets?
(b) How many fruit baskets were sold by Anwar?
(c) The merchants who have sold 600 or more number of baskets are planning to buy a godown for the next season. Can you name them?
From the pictograph, the number of fruit baskets sold by Rahim, Lakhanpal, Anwar, Martin, Ranjit Singh and Joseph are 400, 550, 700, 950, 800 and 450, respectively
(a) Martin sold the maximum number of fruit baskets i.e., 950
(b) Anwar sold 700 fruit baskets
(c) Anwar, Martin and Ranjit Singh are the merchants who sold more than 600 fruit baskets. Hence, these are the merchants who are planning to buy a godown for the next season.
In a Mathematics test, the following marks were obtained by 40 students. Arrange these marks in a table using tally marks.
8 
1 
3 
7 
6 
5 
5 
4 
4 
2 
4 
9 
5 
3 
7 
1 
6 
5 
2 
7 
7 
3 
8 
4 
2 
8 
9 
5 
8 
6 
7 
4 
5 
6 
9 
6 
4 
4 
6 
6 
(a) Find how many students obtained marks equal to or more than 7.
(b) How many students obtained marks below 4?
Marks 
Tally Marks 
Number of Students 

1 
 
2 

2 
 
3 

3 
 
3 

4 
 
7 

5 
 
6 

6 
 
7 

7 
5 

8 
 
4 

9 
 
3 
(a) The students who got marks equal to or more than 7 are the students who got marks as either of 7, 8 and 9. Therefore, number of these students
= 5 + 4 + 3
= 12
(b) The students who got marks below 4 are the students who got marks as either of 1, 2 and 3. Therefore number of these students are
= 2 + 3 + 3
= 8
Following is the choice of sweets of 30 students of Class VI.
Ladoo, Barfi, Ladoo, Jalebi, Ladoo, Rasgulla, Jalebi, Ladoo, Barfi, Rasgulla, Ladoo, Jalebi, Jalebi, Rasgulla, Ladoo, Rasgulla, Jalebi, Ladoo, Rasgulla, Ladoo, Ladoo, Barfi, Rasgulla, Rasgulla, Jalebi, Rasgulla, Ladoo, Rasgulla, Jalebi, Ladoo.
(a) Arrange the names of sweets in a table using tally marks.
(b) Which sweet is preferred by most of the students?
By observing the choice of sweets of 30 students. We may construct the table as shown below:
Sweets 
Tally Marks 
Number of Students 
Ladoo 
 
11 
Barfi 
 
3 
Jalebi 
 
7 
Rasgulla 
 
9 
30 
(b) The highest number of students preferred Ladoos. Hence, Ladoo is the most preferred sweet among students.
Total number of animals in five villages are as follows:
Village A: 80
Village B: 120
Village C: 90
Village D: 40
Village E: 60
Prepare a pictograph of these animals using one symbol
to represent 10 animals and answer the following questions:
(a) How many symbols represent animals of village E?
(b) Which village has the maximum number of animals?
(c) Which village has more animals: village A or village C?
We can draw the pictograph for the given data as shown below
(a) There are 60 animals in village E. So 6 symbols represent animals of village E
(b) Village B has 120 animals which is the maximum number among these villages.
(c) Village A has 80 animals, and village C has 90 animals. Clearly, village C has more animals than village A
Total number of students of a school in different years is shown in the following table
Years 
Number of Students 
1996 
400 
1998 
535 
2000 
472 
2002 
600 
2004 
623 
A. Prepare a pictograph of students using one symbol
to represent 100 students and answer the following questions:
(a) How many symbols represent total number of students in the year 2002?
(b) How many symbols represent total number of students for the year 1998?
B. Prepare another pictograph of students using any other symbol each representing 50 students. Which pictograph do you find more informative?
A
(a) Total number of students in the year 2002 represents 6 symbols
(b) Total number of students in the year 1998 represents 5 complete and 1 incomplete symbols
B. Second is more informative
The bar graph given alongside shows the amount of wheat purchased by the government during the year 19982002.
Read the bar graph and write down your observations. In which year was
(a) the wheat production maximum?
(b) the wheat production minimum?
(a) Wheat production was maximum in the year 2002.
(b) Wheat production was minimum in the year 1998.
Observe this bar graph which shows the marks obtained by Aziz in halfyearly examinations in different subjects. Answer the given questions.
(a) What information does the bar graph give?
(b) Name the subject in which Aziz scored maximum marks.
(c) Name the subject in which he has scored minimum marks.
(d) State the name of the subjects and marks obtained in each of them.
(a) The bar graph shows the marks scored by Aziz in different subjects.
(b) Aziz scored maximum marks in Hindi, i.e., 80 marks.
(c) Aziz scored minimum marks in Social Studies, i.e., 40 marks.
(d) Hindi – 80 marks, English – 60 marks, Mathematics – 70 marks, Science – 50 marks and Social Studies – 40 marks.
Observe this bar graph which shows the sale of shirts in a readymade shop from Monday to Saturday.
Now answer the following questions:
(a) What information does the above bar graph give?
(b) What is the scale chosen on the horizontal line representing the number of shirts?
(c) On which day the maximum number of shirts sold were? How many shirts were sold on that day?
(d) On which day the minimum number of shirts sold were?
(e) How many shirts were sold on Thursday?
(a) The above bar graph shows the number of shirts sold from Monday to Saturday.
(b) 1 unit length = 5 shirts is the scale on the horizontal line representing the number of shirts.
(c) On Saturday, the maximum number of shirts were sold, i.e., 60 shirts were sold.
(d) On Tuesday, the minimum number of shirts were sold, i.e., 10 shirts were sold.
(e) 35 shirts were sold on Thursday.
A survey of 120 school students was done to find which activity they prefer to do in their free time.
Preferred Activity 
Number of Students 
Playing 
45 
Reading story books 
30 
Watching T.V 
20 
Listening to music 
10 
Painting 
15 
Draw a bar graph to illustrate the above data taking a scale of 1 unit length = 5 students. Which activity is preferred by most of the students other than playing?
By taking a scale of 1 unit length = 5 students, the bar graph is shown below considering the above data:
Reading storybooks is the activity preferred by most of the students, other than playing.
The number of Mathematics books sold by a shopkeeper on six consecutive days is shown below:
Days 
Sunday 
Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
Number of books sold 
65 
40 
30 
50 
20 
70 
Draw a bar graph to represent the above information choosing the scale of your choice.
By taking a scale of 1 unit length = 10 books, we can draw a bar graph of the above data as follows:
Following table shows the number of bicycles manufactured in a factory during the years 1998 to 2002. Illustrate this data using a bar graph. Choose a scale of your choice
Year 
Number of Bicycles Manufactured 
1998 
800 
1999 
600 
2000 
900 
2001 
1100 
2002 
1200 
(a) In which year was the maximum number of bicycles manufactured?
(b) In which year was the minimum number of bicycles manufactured?
By taking a scale of 1 unit length = 100 bicycles, we can draw a bar graph of the above data as follows:
(a) In the year 2002, the maximum number of bicycles were manufactured, i.e. 1200 bicycles.
(b) In the year 1999, the minimum number of bicycles were manufactured, i.e. 600 bicycles.
Number of persons in various age groups in a town is given in the following table.
Age Group (in years) 
114 
1529 
3044 
4559 
6074 
75 and above 
Number of Persons 
2 lakhs 
1 lakh 60 thousand 
1 lakh 20 thousand 
1 lakh 20 thousand 
80 thousand 
40 thousand 
Draw a bar graph to represent the above information and answer the following questions. (take 1 unit length = 20 thousand)
(a) Which two age groups have the same population?
(b) All persons in the age group of 60 and above are called senior citizens. How many senior citizens are there in the town?
By taking a scale of 1 unit length = 20 thousand, we can draw a bar graph of the above data as follows:
(a) The two age groups which have the same population are 3044 and 4559.
(b) Senior citizens are the persons between the age group either from 6074 or 75 and above.
Therefore, the number of senior citizens in the town = 80000 + 40000
= 1 lakh 20 thousand
Hence, the number of senior citizens in the town is 1 lakh 20 thousand.
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