Averages
1.Average=Sum of quantities/Number of quantities.
2.Suppose a man covers a certain distance at x kmph and an equal distance at y kmph ,then the average speed during the whole journey is (2xy/x+y) kmph.
Examples:
1.Find the average of all these numbers.142, 147, 153, 165, 157.
Solution:
142 147 153 165 157
Here consider the least number i.e, 142
comparing with others,
142 147 153 165 157
+5 +11 +23 +15
Now add 5+11+23+15 = 52/5 = 10.8
Now add 10.8 to 142 we get 152.8
(Average of all these numbers).
Answer is 152.8
2.Find the average of all these numbers.4,10,16,22,28
Solution:
4, 10, 16, 22, 28
As the difference of number is 6
Then the average of these numbers is central one i.e, 16.
Answer is 16.
3.Find the average of all these numbers.4,10,16,22,28,34.
Solution:
Here also difference is 6.
Then middle numbers 16,22 take average of these
two numbers 16+22/2=19
Therefore the average of these numbers is 19.
Answer is 19.
4.The average marks of a marks of a student in 4 Examination is 40.If he got 80 marks in 5th Exam then what is his new average.
Solution:
4*40+80=240
Then average means 240/5=48.
Answer is 48.
5.In a group the average income of 6 men is 500 and that of 5 women is 280, then what is average income of the group.
Solution:
6*500+5*280=4400
then average is 4400/11=400.
Another Method: here consider for 6 men
6 men - each 500.
so 5th women is 280.
then 500-280=220.
then 220*6/11=120.
therefore 120+280=400.
Answer is 400.
6.The average weight of a class of 30 students is 40 kgs if the teacher weight is included then average increases by 2 kgs then find the weight of the teacher?
Solution:
30 students average weight is 40 kgs.
So,when teacher weight is added it increases by 2 kgs
so total 31 persons ,therefore 31*2=62.
Now add the average weight of all student to it
we get teachers weight i.e, 62+40=102 kgs.
Answer is 102 kgs.
7.The average age of Mr and Mrs Sharma 4 years ago is 28 years. If the present average age of Mr and Mrs Sharma and their son is 22 years. What is the age of their son.
Solution:
4 years ago their average age is 28 years.
So their present average age is 32 years.
32 years for Mr and Mrs Sharma then 32*2=64 years.
Then present age including their son is 22 years.
So 22*3 =66 years.
Therefore son age will be 66-64 = 2 years.
Answer is 2 years.
8.The average price of 10 books is increased by 17 Rupees when one of them whose value is Rs.400 is replaced by a new book. What is the price of new book?
Solution:
10 books Average increases by 17 Rupees
so 10*17= 170.
so the new book cost is more and by adding its cost average
increase,therefore the cost of new book is 400+170=570Rs.
Answer is 570 Rs.
9.The average marks of girls in a class is 62.5. The average marks of 4 girls among them is 60.The average marks of remaining girls is 63,then what is the number of girls in the class?
Solution:
Total number of girls be x+4.
Average marks of 4 girls is 60.
therefore 62.5-60=2.5
then 4*2.5 =10.
the average of remaining girls is 63
here 0.5 difference therefore 0.5*x=10(since we got from 4 girls)
(this is taken becoz both should be equal)
x=10/0.5
x=20.
This clear says that remaining are 20 girls
therefore total is x+4=20+4=24 girls
Answer is 24 girls.
Top
10.Find the average of first 50 natural numbers.
Solution:
Sum of the Natural Numbers is n(n+1)/2
therefore for 50 Natural numbers 50*51/2=775.
the average is 775/50=15.5
Answer is 15.5 .
11.The average of the first nine prime number is?
Solution:
Prime numbers are 2,3,5,7,11,13,17,19,23
therefore 2+3+5+7+11+13+17+19+23=100
then the average 100/9= 11 1/9.
Answer is 11 1/9.
12.The average of 2,7,6 and x is 5 and the average of and the average of 18,1,6,x and y is 10 .what is the value of y?
Solution:
2+7+6+x/4=5
=>15+x=20
=>x=5.
18+1+6+x+y/5=10
=>25+5+y=50
=>y=20.
13.The
average of a non-zero number and its square is 5 times the number.The
number is
Solution:
The number
be x
then
x+x2/2=5x
=>x2-9x=0
=>x(x-9)=0
therefore
x=0 or x=9.
The number
is 9.
14.Nine
persons went to a hotel for taking their meals . Eight of them spent
Rs.12 each on their meals and the ninth spent Rs.8 then the average expenditure of all the nine. What was the total money spent by
them?
Solution:
The average
expenditure be x.
then
8*12+(x+8)=9x
=>96+x+8=9x.
=>8x=104
=>x=13
Total money
spent =9x=>9*13=117
Answer is
Rs.117
15.The
average weight of A.B.C is 45 Kgs.If the average weight of A and B be
40 Kgs and that of Band C be 43 Kgs. Find the weight of B?
Solution:
The weight
of A,B,Care 45*3=135 Kgs.
The weight
of A,B are 40*2=80 Kgs.
The weight
of B,C are 43*2=86 Kgs.
To get the
Weight of B.
(A+B)+(B+C)-(A+B+C)=80+86-135
B=31 kgs.
Answer is
31 Kgs.
16.The sum
of three consecutive odd number is 48 more than the average of these
number .What is the first of these numbers?
Solution:
let the
three consecutive odd numbers are x, x+2, x+4.
By adding
them we get x+x+2+x+4=3x+6.
Then
3x+6-(3x+6)/3=38(given)
=>2(3x+6)=38*3.
=>6x+12=114
=>6x=102
=>x=17.
Answer is
17.
17.A family
consists of grandparents,parents and three grandchildren. The average
age of the grandparents is 67 years,that of parents is 35 years and
that of the grand children is 6 years . What is the average age of the
family?
Solution:
grandparents
age is 67*2=134
parents age
is 35*2=70
grandchildren
age is 6*3=18
therefore
age of family is 134+70+18=222
average is
222/7=31 5/7 years.
Answer is
31 5/7 years.
18.A
library has an average of 510 visitors on Sundays and 240 on other days
.The average number of visitors per day in a month 30 days
beginning with a Sunday is?
Solution:
Here
specified that month starts with Sunday
so, in a
month there are 5 Sundays.
Therefore
remaining days will be 25 days.
510*5+240*25=2550+6000
=8550
visitors.
The average
visitors are 8550/30=285.
Answer is
285.
19.The
average age of a class of 39 students is 15 years. If the age
of the teacher be included ,then average increases
by 3 months. Find the age of the teacher.
Solution:
Total age for 39 persons is 39*15=585 years.
Now 40
persons is 40* 61/4=610 years
(since 15
years 3 months=15 3/12=61/4)
Age of the
teacher =610-585 years
=>25
years.
Answer is
25 years.
20.The
average weight of a 10 oarsmen in a boat is increasesby 1.8 Kgs
.When one of the crew ,who weighs 53 Kgs is replaced by
new man. Find the weight of the new man.
Solution:
Weight of 10 oars men is increases by 1.8 Kgs
so,
10*1.8=18 Kgs
therefore
53+18=71 Kgs will be the weight of the man.
Answer is
71 Kgs.
21.A bats
man makes a score of 87 runs in the 17th inning and thus
increases his average by 3. Find the average after 17th
inning.
Solution:
Average after 17 th inning =x
then for
16th inning is x-3.
Therefore
16(x-3)+87 =17x
=>x=87-48
=>x=39.
Answer is
39.
22.The
average age of a class is 15.8 years .The average age of boys in
the class is 16.4 years while that of the girls is 15.4
years .What is the ratio of boys to girls in the class.
Solution:
Ratio be k:1 then
k*16.4 +
1*15.4 = (k+1)*15.8
=>(16.4-15.8)k=15.8-15.4
=>k=0.4/0.6
=>k=2/3
therefore
2/3:1=>2:3
Answer is
2:3
23.In a
cricket eleven, the average of eleven players is 28 years
.Out of these, the average ages of three groups of players
each are 25 years, 28 years and 30 years respectively.
If in these groups, the captain and the youngest
player are not included and the captain is eleven
years older than the youngest players,
what is the
age of the captain?
Solution:
let the age of youngest player be x
then ,age
of the captain =(x+11)
therefore
3*25 + 3*28 + 3*30 + x + x+11=11*28
=>75+84+90+2x+11=308
=>2x=48
=>x=24.
Therefore
age of the captain =(x+11)= 24+11= 35 years.
Answer is
35 years.
24.The
average age of the boys in the class is twice the number
of girls in the class .If the ratio of boys and
girls in the class of 36 be 5:1, what is the total
of the age (in years) of the boys in the class?
Solution:
Number of boys=36*5/6=30
Number of
girls =6
Average age
of boys =2*6=12 years
Total age
of the boys=30*12=360 years
Answer is
360 years.
25.Five
years ago, the average age of P and Q was 15 years
,average age of P,Q, and R today is 20
years,how old will R be after 10 years?
Solution:
Age of P and Q are 15*2=30 years
Present age
of P and Q is 30+5*2=40 years.
Age of P Q
and R is 20*3= 60 years.
R ,present
age is 60-40=20 years
After 10
years =20+10=30 years.
Answer is
30 years.
26.The
average weight of 3 men A,B and C is 84 Kgs. Another man
D joins the group and the average now becomes 80
Kgs.If another man E whose weight is
3 Kgs more
than that of D ,replaces A then the average
weight B,C,D and E becomes 79 Kgs,find the weight
of A is?
Solution: Total
weight of A, B and C is 84 * 3 =252 Kgs.
Total
weight of A,B,C and Dis 80*4=320 Kgs
Therefore
D=320-252=68 Kgs.
E weight
(68+3)=71 kgs
Total
weight of B,C,D and E = 79*4=316 Kgs
(A+B+C+D)-(B+C+D+E)=320-316
=4Kgs
A-E=4Kgs
A-71=4 kgs
A=75 Kgs
Answer is
75 kgs
27.A team
of 8 persons joins in a shooting competition. The best
marksman scored 85 points.If he had scored 92 points
,the average score for the team would have been
84.The team scored was.
Solution:
Here consider the total score be x.
therefore
x+92-85/8=84
=>x+7=672
=>x=665.
Answer is
665
28.A man
whose bowling average is 12.4,takes 5 wickets for 26 runs
and there by decrease his average by 0.4. The number
of wickets,taken by him before his last match is:
Solution:
Number of wickets taken before last match be x.
therefore
12.4x26/x+5=12(since average decrease by 0.4
therefore
12.4-0.4=12)
=>12.4x+2612x+60
=>0.4x=34
=>x=340/4
=>x=85.
Answer is
85.
29.The mean
temperature of Monday to Wednesday was 37 degrees and of
Tuesday to Thursday was 34 degrees .If the temperature
on Thursday was 4/5th that of Monday. The
temperature on Thursday was?
Solution:
The total
temperature recorded on Monday,Wednesday was 37*3=111.
The total
temperature recorded on Tuesday,
Wednesday,Thursday
was 34*3=102.
and also
given that Th=4/5M
=>M=5/4Th
(M+T+W)-(T+W+Th)=111-102=9
M-Th=9
5/4Th-Th=9
Th(1/4)=9
=>Th=36
degrees.
30. 16
children are to be divided into two groups A and B of 10 and 6
children. The average percent marks obtained by the
children of group A is 75 and the average percent marks of
all the 16 children is 76. What is the average percent
marks of children of groups B?
Solution:
Here given average of group A and whole groups .
So,(76*16)-(75*10)/6
=>1216-750/6
=>466/6=233/3=77
2/3
Answer is
77 2/3.
31.Of the
three numbers the first is twice the second and the second
is twice the third .The average of the reciprocal of the
numbers is 7/72, the number are.
Solution:Let
the third number be x
Let the
second number be 2x.
Let the
first number be 4x.
Therefore
average of the reciprocal means
1/x+1/2x+1/4x=(7/72*3)
7/4x=7/24
=>4x=24
x=6.
Therefore
First
number is 4*6=24.
Second
number is 2*6=12
Third
number is 1*6=6
Answer is
24,12,6.
32.The
average of 5 numbers is 7.When 3 new numbers are added
the average of the eight numbers is 8.5. The average
of the three new number is?
Solution:
Sum of three new numbers=(8*8.5-5*7)=33
Their
average =33/3=11.
Answer is
11.
33.The
average temperature of the town in the first four days
of a month was 58 degrees. The average for the
second, third, fourth and fifth days was
60 degree
.If the temperature of the first and fifth days
were in the ratio 7:8 then what is the
temperature on the fifth day?
Solution :
Sum of
temperature on 1st 2nd 3rd
and 4th
days =58*4=232 degrees.
Sum of
temperature on 2nd 3rd 4th
and 5th
days =60*4=240 degrees
Therefore
5th day temperature is 240-232=8 degrees.
The ratio
given for 1st and 5th days be 7x and 8x degrees
then
8x-7x=8
=>x=8.
therefore
temperature on the 5th day =8x=8*8=64 degrees.
