Kerala Syllabus 6th Standard Maths Solutions Chapter 2 Average

Kerala State Syllabus 6th Standard Maths Solutions Chapter 2 Average

Average Text Book Questions and Answers

Donation math Textbook Page No. 19

Children in class 6A decided to raise 1000 rupees to buy books for the library. There are 40 children in the class. And they decided that all of them should give the same amount. How much should each give?
To compute this, we need only divide 1000 by 40, right?

There are 30 children in class 6B. They raised 1200 rupees for a medical fund. Can you calculate how much each gave?

Here, the amounts given may not be the same. So, we cannot say exactly how much each gave.

Yet, we can say something about the amount each gave.
If all had given the same amount, each would have given 40 rupees.
If all had given less than 40 rupees, they could not have raised 1200 rupees.
In the same way, all could not have given more than 40 rupees.
So, we can say something like these:

If all had given the same amount, then each would have given 40 rupees; if some had given less than 40 rupees, then some others must have given more than 40 rupees.
Here we say that the average amount each kid gave is 40 rupees.

Average problems

Manikuttan supplies milk to the society each day. Last week, he supplied 56 litres in all. How much did he give each day of this week on average?

The amount given on all days may not be the same. Average per day means how much he would have given each day, had he given the same amount on all days. So, the average in this case is 56 ÷ 7 = 8 litres.

As mentioned at the beginning, this does not mean he supplied exactly 8 litres each day.
It might be 7 litres one day and 9 litres another day. It might be slightly more or less than 8 litres each day.
But it is very much unlikely that he gave only 1 litre one day and 15 litres another day.

On five days, a man spends 300 rupees, 250 rupees, 270 rupees, 280 rupees and 290 rupees. How much did he spend each day on average?
Given that: A man had spent 300 rupees, 250 rupees, 270 rupees, 280 rupees and 290 rupees in 5 days.
The average amount spent by the man can be calculated by dividing the total amount he had spent in 5 days.
Total amount=300+250+270+280+290=1390 rupees.
So, the average amount spent each day will be 1390÷5=278 rupees.
This does not mean that he had spent 278 rupees daily. This is the average of his total expenditure.

How much did he spent in all?
The total amount spent in five days will be sum of all the amounts spent during this period.
Total amount=300+250+270+280+290=1390 rupees.

And in how many days?
The man had spent the total amount,1390 rupees in 5 days.

To get the average expenditure per day, we have to divide the total amount spent by the number of days.
See the length of cloth needed to make shirts for some kids in Sudheer’s class.

There are 23 boys in the class. How much should be bought to make shirts for all?
How do we compute this?

If the length of cloth is the same for all, we can calculate exactly how much is for 23 kids.
By the table, the total length needed for five is 600 centimetres.
If it is the same amount for all, we can say each needs 120 centimetres.
In other words, the average length needed for each is 120 centimetres.

We can use the average length of 120 centimetre to calculate the total length of cloth needed. But would it be right to cut out a 120 centimetre piece for each?

Since they are all in the same class, there wouldn’t be much difference among the lengths needed for them.
So, we can estimate the total length of cloth needed as 23 × 120 centimetres = 2760 centimetres. or 27 metres and 60 centimetres.

Textbook Page No. 22

Question 1.
The number of children who attended class from Monday to Friday are 34, 35, 32, 33, 31. What is the average number of children who attended classes each day?
Given that: The number of children attended class from Monday to Friday are 34, 35, 32, 33, 31.
Step 1: The total strength who attended class from Monday to Friday will be 34+35+32+33+31=165
Step 2: The average number of students for this week can be calculated by dividing the total strength by number of days. Therefore, the average will be 165÷5=33.
The number of children attending class may not be the same on all the days. Average per day means how many children would have attended each day.So, this does not mean 33 children attended each day.It might be 30 students attending on monday while 25 on tuesday. It might be slightly more or less than 33 students each day.

Question 2.
The table shows the amount of electricity used in Majeed’s house for some months. What is the average amount of electricity used per month? Which are the months on which usage is more than the average?

Given that: The amount of electricity spent in 5 months.
Step 1: The total amount of electricity spent can be calculated by adding the units spent in all the months.So, it will be 85+90+75+82+78=410 units.
Step 2: The average amount of electricity spent in 5 months can be calculated by dividing the total units spent in 5 months.Therefore, the average amount of electricity used per month will be 410÷5=82 units.
Step 3: In January and February the amount of electricity usage is more than the average.
In April, it is same as of the average units.While in March and May, it is less than the average units.

Question 3.
The weights of players in a team are 68 kilograms, 72 kilograms, 80 kilograms, 70 kilograms, 60 kilograms, 70 kilograms. What is the average weight of a player in the team?
Given that: The weights of players in a team are 68 kilograms, 72 kilograms, 80 kilograms, 70 kilograms, 60 kilograms, 70 kilograms.
Step 1:The total weight of all the players will be 68+72+80+70+60+70=420 kilograms.
Step 2: To get the average weight, we need to divide the total weight by number of players.Therefore, it will be 420÷6=70 kilograms.

Question 4.
The total income of a man in 8 days is 1840 rupees. What is his average income per day?
GIven that: The total income of a man in 8 days is 1840 rupees.
Step 1: Total income for 8 days is 1840 rupees.
Step 2: To calculate the average income per day, we need to divide the total income by number of days.Therefore, the average income will be 1840÷8=230 rupees.
The income earned may or may not be the same on all the days. It might be slightly more or less than 230 rupees each day or can also be 230 rupees each day.

Which is better?

Ouseph and Abu grow different types of coconut trees. Ouseph has 20 trees and Abu has 18. See how many coconuts each got last year:

Which kind gives more coconuts?
Given that: The number of coconuts got in january,april,august and november.
Step 1: The total number of coconuts Ouseph got will be 160+280+200+260=900 coconuts.
Step 2: The total number of coconuts Abu got will be 200+264+240+160=864 coconuts.
By observing the figures above, we can say that Ouseph got more coconuts than Abu.

Can we decide this by comparing just the total numbers each got?
Yes, by observing the total number of coconuts, we can decide who got more coconuts.
In this scenario Ouseph got 36 more coconuts than Abu.

So, how do we decide?
Let’s compute the average number of coconuts per tree for each kind.

How many coconuts per tree did Ouseph got on average?
Given that: The total number of coconuts got from 20 Ouseph kind is 900.
Step 1:To calculate the average number of coconuts per tree, we need to divide the total number of coconuts with the number of trees.
Therefore, the average number of coconuts got per tree will be 900÷20=45.

And Abu?
Given that: The total number of coconuts got from 18 Abu kind is 864.
Step 1:To calculate the average number of coconuts per tree, we need to divide the total number of coconuts with number of trees.
Therefore, the average number of coconuts got per tree will be 864÷18=48.

Computing like this, we can decide which kind of tree gives better yield.
Yes, from the average number of coconuts we can decide which kind of tree gives better yield.
Here Abu kind yields more than the Ouseph.

Question 1.
During the Forest Fest celebration, two divisions of class V decided to plant trees as a Haritha Club activity. 35 children of class VA planted 245 saplings and 30 children of class VB planted 240. On the basis of average number of saplings planted per kid, which division did a better job?
Given that: 35 children of class VA planted 245 saplings and 30 children of class VB planted 240.
Step 1: To calculate the average saplings of VA, we need to divide the total number of saplings with the total number of children.
Therefore, the average saplings of VA children will be 245÷35=7.
Step 2:To calculate the average saplings of VB, we need to divide the total number of saplings with the total number of children.
Therefore, the average saplings of VB children will be 240÷30=8.
From the above figures, we can say that VB division did better job by sapling more than VA.

Question 2.
The table shows the number of members and the amount of water used in a month of three households:

How much water did one person in the first household use on average?
Given that: In the first household 18000 litres of water was used in a month by 6 members.
Step 1: To calculate the average usage of water by 1 person, we need to divide the total water used by the members.
Therefore, the average will be 18000÷6=3000 litres.
The water used may not be the same by each family member. It might be slightly more or less than 3000 litres per person in a month.

Given that: In the second household 16000 litres of water was used in a month by 4 members.
Step 1: To calculate the average usage of water by 1 person, we need to divide the total water used by the members.
Therefore, the average will be 16000÷4=4000 litres.
The water used may not be the same by each family member. It might be slightly more or less than 4000 litres per person in a month.

Given that: In the third household 16500 litres of water was used in a month by 5 members.
Step 1: To calculate the average usage of water by 1 person, we need to divide the total water used by the members.
Therefore, the average will be 16500÷5=3300 litres.
The water used may not be the same by each family member. It might be slightly more or less than 3300 litres per person in a month.

According to these figures, in which household used most water per person?
The average amount of water used by each member of first household is 3000 litres.
The average amount of water used by each member of second household is 4000 litres.
The average amount of water used by each member of third household is 3300 litres.
From the above figures, we can say that the second household has used most water per person.

Some other problems

Milk math

Ramu checked his sale of milk for some days and calculated the average income to be 150 rupees per day. If he continues like this, how much can he expect from the sale of milk in June?
There are 30 days in June. So if we get 150 rupees per day on average during the month, he would get 150 × 30 = 4500 rupees.

Trade math Textbook Page No. 24

The incomes for five days of a trade are 6435 rupees, 6927 rupees, 6855 rupees, 7230 rupees and 6562 rupees. After the sixth day, he calculated the average income as 6500 rupees per day. How much did he get on the sixth day?
The amount got each day for the first 5 days is given. Adding all these, we can get the total income for these 5 days. Since the average income is 6500 rupees per day for the first six days, the total income can be calculated by multiplying by 6. Now can’t we find the income on the sixth day?
Given that:The incomes for five days of a trade are 6435 rupees, 6927 rupees, 6855 rupees, 7230 rupees and 6562 rupees and the average income is 6500 rupees per day for the first six days.
Step 1: The total income for first five days will be 6435+6927+6855+7230+6562=34009 rupees.
Step 2: To calculate the total income for six days, we need to multiply the average income with the total number of days.Therefore, the total income for first six days will be 6500×6=39000 rupees.
Step 3: To get the sixth day income, we need to subtract the total income of five days from the total income of six days. So, the sixth day income will be 39000-34009=4991 rupees.

Question 1.
Children were asked to donate books to the school library. Using the given details, fill up the table below.

6B:
To calculate the average of 6B students, we need to divide the number of books by number of children.
Therefore, the average books donated by 6B children will be 240÷40=6.
6C:
To calculate the number of children in 6C, we need to divide the number of books by the average number of books.
Therefore, the average books donated by 6C children will be 175÷5=35.
6D:
To calculate the number of books in 6D, we need to multiply the number of children with the average number of books.
Therefore, the average books donated by 6D children will be 32×10=320.

The sum of 7 consecutive natural numbers is 70. What are the numbers? The sum of 8 consecutive natural number is 92. What are the numbers? Can the sum of 9 consecutive numbers be 58?
Case 1:
Given that: The sum of 7 consecutive natural numbers is 70.
Step 1: Let us assume the first natural number be ‘a’.Now, the other six consecutive numbers will be a+1,a+2,a+3,a+4,a+5 and a+6.
Given that the sum is 70. So, a+a+1+a+2+a+3+a+4+a+5+a+6=70
7a+21=70
7a=70-21
7a=49
a=$$\frac{49}{7}$$
a=7
Therefore, the required number is 7 and the other consecutive numbers are 8,9,10,11,12 and 13.

Case 2:
Given that: The sum of 8 consecutive natural numbers is 92.
Step 1: Let us assume the first natural number be ‘a’.Now, the other six consecutive numbers will be a+1,a+2,a+3,a+4,a+5,a+6 and a+7.
Given that the sum is 92. So, a+a+1+a+2+a+3+a+4+a+5+a+6+a+7=92
8a+28=92
8a=92-28
8a=64
a=$$\frac{64}{8}$$
a=8
Therefore, the required number is 8 and the other consecutive numbers are 9,10,11,12,13,14 and 15.

Case 3:
Given that: The sum of 9 consecutive natural numbers is 58.
Step 1: Let us assume the first natural number be ‘a’.Now, the other six consecutive numbers will be a+1,a+2,a+3,a+4,a+5,a+6,a+7 and a+8.
Given that the sum is 92. So, a+a+1+a+2+a+3+a+4+a+5+a+6+a+7+a+8=58
9a+36=58
9a=58-36
9a=22
a=$$\frac{22}{9}$$
a=2.44
The sum of 9 consecutive natural numbers cannot be 58 as the numbers obtained will not give the sum 58.

Question 2.
The average age of a child in a class of 35 is 11. The average age, including the teacher is 12. How old is the teacher?
Given that:The average age of a child in a class of 35 is 11.The average age, including the teacher is 12.
Step 1: The number of students in a class are 35 and their average age is 11.So, the age of class will be 35×11=385
Step 2: The age of 35 students and a teacher i.e. 36 members is 12. So, the age of class will be 36×12=432
Step 3: Therefore, the age of a teacher can be calculated by subtracting the students age from total. So, it will 432-385=47.
The teacher is 47 years old.

Question 3.
The average weight of a kid in a group of 10 is 35 kilograms. When Sonu also joined them, the average became 36 kilograms. How much does Sonu weigh?
Given that:The average weight of a kid in a group of 10 is 35 kilograms.When Sonu joined, the average of 11 kids became 36.
Step 1: The total weight of 10 kids will be 10×35=350 kilograms.
Step 2: After sonu joined, the total weight of 11 kids will be 11×36=396 kilograms.
Step 3: So, the weight of Sonu can be calculated by subtracting the total weight of 10 kids from the total weight of 11 kids. Therefore, the total weight of sonu is 396-350=46 kilograms.

Question 4.
There are 8 teachers in a school. When a 35 year old teacher was transferred and another teacher joined, the average age ws increased by 2 years. How old is the new teacher?
Given that:There are 8 teachers in a school. When a 35 year old teacher was transferred and another teacher joined, the average age ws increased by 2 years.
Explanation:
Step 1:
Let us assume the age of 7 teachers be ‘a’ and a 35 year old teacher was transferred. The total age of 8 teachers will be a+35.
Let us assume the average age of 8 teachers be x.
x = $$\frac{(a+35)}{8}$$
8x=a+35
8x-35=a                                          (1)
Step 2:
After the new teacher joined, the average age was increased by 2 years which is x+2.
The new average age will be $$\frac{a+age of New teacher}{8}$$=x+2
a+New teacher’s age=8(x+2)
a+New teacher’s age=8x+16         (2)
Step 3:
Substitute the value of a from (1) in (2)
8x-35+New teacher’s age=8x+16
New teacher’s age=8x+16-8x+35
New teacher’s age=8x-8x+16+35
New teacher’s age=0+16+35
New teacher’s age=51
Therefore, the age of new teacher will be 51 years old.

Question 5.
The average rainfall per month during 2014 in a place was calculated to be 23 centimetres. The total rainfall there during June, July and August was 150 centimetres.

i) What is the average rainfall per month during these three months?
Given that: The total rainfall during June, July and August was 150 centimetres.
Explanation:
The average rainfall during these three months will be 150÷3=50 centimetres.

ii) What was the total rainfall during the entire year of 2014?
The total rainfall during the entire year or 12 months will be 23×12=276 centimetres.

iii) What is the average rainfall per month during the other 9 months?
Step 1: The total rainfall of 9 months can be calculated by subtracting the total rainfall of 3 months from the total rainfall of 12 months.
Therefore, the total rainfall per month during the other 9 months will be 276-50=226 centimetres.
Step 2: The average rainfall per month during the other 9 months will be 226÷9=75.33 centimetres.

Question 6.
When a person calculated his expenses from Sunday to Thursday, he found the average expenditure to be 400 rupees per day. Including Friday, the average increased to 430 rupees per day. How much did he spent on Friday?
Given that:
The average expenditure from Sunday to Thursday is 400 rupees per day.
The total sum for five days will be 400×5=2000 rupees.
The average increased to 430 rupees per day. Therefore, the total sum for six days will be 430×5=2580 rupees.
Therefore, the money he spent on friday will be the amount obtained after subtracting the total five days sum from the total six days sum,which is 2580-2500=580 rupees.
So, he had spent 580 rupees on friday.

Including Saturday, the average decreased to 390 rupees per day. How much did he spend on Saturday?
The total expenditure from sunday to saturday will be 390×7=2730 rupees.
The total amount spent on saturday will be 2730-2580=150 rupees.

Question 7.
40 children of class VI donated 50 rupees on average to the Mutual Aid Fund. 30 children of class V donated 800 rupees in all. If we consider both classes together, how much did each donate on average?
Given that: 40 children of class VI donated 50 rupees on average to the Mutual Aid Fund. 30 children of class V donated 800 rupees in all.
Step 1: 40 students of class VI donated 50 rupees on average. So, the total amount donated will be 50×40=2000 rupees.
Step 2: 30 student of class V donated 800 rupees in all. Therefore, the total amount spent by both class V and class VI students will be 2000+800=2800 rupees.
Step 3: To calculate the average amount of money donated by each student, we need to divide the total sum by the total number of students.
Therefore, the average amount will be 2800÷70=40.
On an average each children donated 40 rupees. If all had given the same amount, then each would have given 40 rupees; if some had given less than 40 rupees, then some others must have given more than 40 rupees.

Question 8.
Three groups of 10 kids. The average weight of a kid in each group is 35 kilograms. One more kid joined each group.

i) The average weight of a kid in the first group is still 35 kilograms.
Total number of kids in 3 groups will be 10×3=30 students.
The average weight of 30 kids in each group will be 10×35=350 kilograms.
One more kid joined in first group. So, the total weight of 31 stuudents will be 31×35=385 kilograms.

ii) The average weight of a kid in the second group is now 36 kilograms.
One more kid joined in second group. So, the total weight of 31 stuudents will be 31×36=396 kilograms.

iii) The average weight of a kid in the third group is now 34 kilograms.
One more kid joined in third group. So, the total weight of 31 stuudents will be 31×34=374 kilograms.

Compute the weight of the new kid in each group.
The weight of the new kid in first group will be 385-350=35 kilograms.
The weight of the new kid in second group will be 396-350=46 kilograms.
The weight of the new kid in third group will be 374-350=24 kilograms.

In your class, are the boys or girls taller on average? Calculate the average height, considering all kids in the class. Compare it with the average height of boys and girls.
Assumed data:
Height of class VIA girls is 100cm,102cm,96cm,98cm,104cm,75cm,85cm,95cm,97cm,83cm and 115cm.
Height of class VIA boys is 101cm,92cm,99cm,85cm,98cm,80cm,95cm,89cm,121cm,115cm and 125cm.
Explanation:
The average height of class VIA will be the total sum of student’s height divided by the total number of students. Therefore, the average the height of VIA class will be 2150÷20=107.5cm
The average height of class VIA girls will be 1050÷10=105cm
The average height of class VIA boys will be 1100÷10=110cm
From the figures we can say that the average height of boys is more than that of girls.

Write any five consecutive natural numbers and find their sum. Does the middle number have any relation with the sum? What if we take 9 consecutive natural numbers? Does the same relation hold for any odd number of numbers?
What if the number of numbers is even?
How about taking consecutive odd numbers or consecutive even numbers?
Assumed data: Let us assume the five consecutive natural numbers be 2,3,4,5 and 6.
Case 1: The sum of the assumed five consecutive natural numbers will be 2+3+4+5+6=20.
The average of the five consecutive natural numbers will be 20÷5=4.
The average of five consecutive natural numbers is equal to the middle number.
Thus, the middle number is equal to the average of the consecutive odd numbers.

Case 2: The sum of the assumed nine consecutive natural numbers will be 1+2+3+4+5+6+7+8+9=45.
The average of the nine consecutive natural numbers will be 45÷9=5.
The average of nine consecutive natural numbers is equal to the middle number.
Thus, the middle number is equal to the average of the consecutive odd numbers.

Case 3: The sum of the assumed four consecutive natural numbers will be 1+2+3+4=10.
The average of the four consecutive natural numbers will be 10÷4=2.5.
In case of consecutive even numbers, the average of four consecutive natural numbers is not equal to the middle number.