33 AVERAGES& AGES
wnat is average
The concept of average is equal distribution of the overall value among all the things or persons present
there. So the formula for finding the average is as follows:
Average, A-Total ofallthings, T/ Number ofthings, N
Thercfore, Total, T=AN
Ifany person joins a group with more value than the average ofthe group then the overall average increases.
This is because the value in excess than the average will also be distributed equally among all the members.
Similarly when any value less than the average joins the group the overall group decreases as the deficit is
divided cqually anong all the people present there.
Example:
Consider three people A, B and C with total of Rs. 30/-. Their average becomes Rs. 10/- for each. If
another person Djoins them with Rs. 50- then he has Rs. 40/- morethan actual average ofRs. 10/-.
So this Rs. 40/- will get distributed among those four and each gets Rs. 10/- Thus the average becomes Rs.
20/-cach.
Example:
The average age ofa class of30 students is 12. Ifthe teacher is also included the
average becomes 13 years.
Find the teacher's age.
Soln:
When the teacher is included there are totally 31 members in the class and the average is increased by 1
year. This means that everyone got 1 extra year after distributing the extra years ofthe teacher.
So extra years ofthe teacher are as follow: 3Ixl=31 years.
Age ofthe teacher = actual avg + extra years= 12+31 =43 years.
EXERCISE:
. Ihe average of 13 papers is 40. The average ofthe first 7 papers is 42 and ofthe last seven papers is 35.
Find the marks obtained in the 7th paper?
(A) 23 (B) 38
(C) 19 (D) None ofthese
, 2 ne average age ofthe Indian cricket team playing the Nagpur test is 30. The average age of5 ofthen
is 27 and that ofanother set ofS players, tolally different from the first five, is 29. Ifit is the captainwhoplawayer
not included in either ofthese two groups, then find the age ofthe captain.
(A) 75 (B) 55
(C) 50 (D) Cannot be determined
3. A bus goes to Ranchi from Patna at the rate of60 km per hour. Another bus leaves Ranchi for Patna a t
same times as the first bus at the rate of 70 km per hour. Find the average speed for the journeys ofthe t
buses combined ifit is known that the distance from Ranchi to Patna is 420 kilometers.
(A) 64.615 kmph (B) 64.5 kmph
(C)63.823kmph (D) 64.82 kmph
Atrain travels 8 km inthe first quarter of an hour, 6 km in the second quarter and 40 km in the third quart
rl
Find the average speed of the train
per hour over the entirejourney.
(A) 72 km/h (B) 18 km/h
(C) 77.33 km/h D) 78.5 km/h
5. The average weight of6 men is 68.5 kg. Ifl is known that Ram and Tram weigh 60 kg each, find the avera
weight ofthe others.
(A) 72.75 kg (B) 75 kg
(C) 78 kg (D) None of these
6. The average scoreofa class of40 students is 52. What will be the average score ofthe rest ofthe studen
ifthe average score of 10 ofthe students is 61.
(A) 50 (B) 47
(C) 48 (D) 49
1. The average age of 80 students of IIM, Bangalore of the 1995 batch is 22 vears. What will be the n
average if we include the 20 faculty members whose average age is 37 years?
(A) 32 years (B) 24 years
(C) 25 years (D) None of these
8. Out ofthe three numbers, the first is twice the second and three times
the third. The average of the u
numbers is 88. The smallest number is
(A) 72
(B) 36
(C) 42
(D) 48
9 The sum of three numbers is 98. Ifthe ratio
between the first and second is 2:3 and that betweenthe*
seco
and the third is 5 :8, then the second number
is
wnat is average
The concept of average is equal distribution of the overall value among all the things or persons present
there. So the formula for finding the average is as follows:
Average, A-Total ofallthings, T/ Number ofthings, N
Thercfore, Total, T=AN
Ifany person joins a group with more value than the average ofthe group then the overall average increases.
This is because the value in excess than the average will also be distributed equally among all the members.
Similarly when any value less than the average joins the group the overall group decreases as the deficit is
divided cqually anong all the people present there.
Example:
Consider three people A, B and C with total of Rs. 30/-. Their average becomes Rs. 10/- for each. If
another person Djoins them with Rs. 50- then he has Rs. 40/- morethan actual average ofRs. 10/-.
So this Rs. 40/- will get distributed among those four and each gets Rs. 10/- Thus the average becomes Rs.
20/-cach.
Example:
The average age ofa class of30 students is 12. Ifthe teacher is also included the
average becomes 13 years.
Find the teacher's age.
Soln:
When the teacher is included there are totally 31 members in the class and the average is increased by 1
year. This means that everyone got 1 extra year after distributing the extra years ofthe teacher.
So extra years ofthe teacher are as follow: 3Ixl=31 years.
Age ofthe teacher = actual avg + extra years= 12+31 =43 years.
EXERCISE:
. Ihe average of 13 papers is 40. The average ofthe first 7 papers is 42 and ofthe last seven papers is 35.
Find the marks obtained in the 7th paper?
(A) 23 (B) 38
(C) 19 (D) None ofthese
, 2 ne average age ofthe Indian cricket team playing the Nagpur test is 30. The average age of5 ofthen
is 27 and that ofanother set ofS players, tolally different from the first five, is 29. Ifit is the captainwhoplawayer
not included in either ofthese two groups, then find the age ofthe captain.
(A) 75 (B) 55
(C) 50 (D) Cannot be determined
3. A bus goes to Ranchi from Patna at the rate of60 km per hour. Another bus leaves Ranchi for Patna a t
same times as the first bus at the rate of 70 km per hour. Find the average speed for the journeys ofthe t
buses combined ifit is known that the distance from Ranchi to Patna is 420 kilometers.
(A) 64.615 kmph (B) 64.5 kmph
(C)63.823kmph (D) 64.82 kmph
Atrain travels 8 km inthe first quarter of an hour, 6 km in the second quarter and 40 km in the third quart
rl
Find the average speed of the train
per hour over the entirejourney.
(A) 72 km/h (B) 18 km/h
(C) 77.33 km/h D) 78.5 km/h
5. The average weight of6 men is 68.5 kg. Ifl is known that Ram and Tram weigh 60 kg each, find the avera
weight ofthe others.
(A) 72.75 kg (B) 75 kg
(C) 78 kg (D) None of these
6. The average scoreofa class of40 students is 52. What will be the average score ofthe rest ofthe studen
ifthe average score of 10 ofthe students is 61.
(A) 50 (B) 47
(C) 48 (D) 49
1. The average age of 80 students of IIM, Bangalore of the 1995 batch is 22 vears. What will be the n
average if we include the 20 faculty members whose average age is 37 years?
(A) 32 years (B) 24 years
(C) 25 years (D) None of these
8. Out ofthe three numbers, the first is twice the second and three times
the third. The average of the u
numbers is 88. The smallest number is
(A) 72
(B) 36
(C) 42
(D) 48
9 The sum of three numbers is 98. Ifthe ratio
between the first and second is 2:3 and that betweenthe*
seco
and the third is 5 :8, then the second number
is
