The document contains several word problems involving calculating averages. 1) The average age of 4 family members is 25 years. If the head is included, the average increases by 20%. The age of the head is calculated to be 50 years. 2) A man travels the same total distance divided into 3 parts at speeds of 15 km/h, 10 km/h, and 5 km/h. His average speed for the whole journey is calculated to be 8.18 km/h. 3) Given information about distances traveled and speeds, the average speed of a person is calculated in one example as 5 9/11 km/h.

1. AVERAGE
STANDARD LEVEL
C.S.VEERARAGAVAN
APTITUDE TRAINER
1

2. Average increase %
• The average age of 4 member of a family is 25 yr. If head of the family is included
in this group then average age increase by 20%. Find out the age of the head.
A)45 yr B)50 yr C)55 yr D)60 yr
• Total age of 4 member = 25 x 4 = 100 yr
• Total age of 5 members including the head
• = 5 x (25 + 25 x 20/100)
• = 5 x 30
• = 150 yr
• ∴ Age of the head = 150 - 100 = 50 yr
2

3. AVERAGE SPEED
A man divides his total route
of journey into three equal
parts and decide to travel the
three parts with
speed of 15 km/h, 10 km/h
and 5 km/ h respectively.
Find his average speed of
during journey.
a)2.28 km/h b)9km/h
c)14 km/h d)8.18 km /h
3
If three equal distances are covered at
different speeds of A, B and C km/h,
respectively, then average speed during
whole journey
=
3ABC
AB+ BC + CA
km/h
∴ Required average speed
=
3 X 15 X 10 X 5
(15 X 10) + (10 X 5) + (15 X 5)
=
3X 15 X 10 X 5
150 + 50 + 75
= 8.18 km/h

4. AVERAGE after removing few
• The average of 50 numbers is 38.
• If the two numbers 45 and 55 are not considered,
• What will be the average of remaining numbers?
A)36.5 B)37 C)37.5 D)37.52
Sum of 50 numbers = 50 * 38 = 1900
Sum of not considered numbers = 45+55= 100
Sum of 48 numbers = 1800
Average of remaining numbers =
1800
48
=
225
6
= 37.5
4

5. Average increase
• The average age of 4 member of a family is 25 yr.
• If head of the family is included in this group then
• average age increase by 20%.
• Find out the age of the head.
a)45 yr b)50 yr c)55 yr d)60 yr
• Sum of age of members = 4 * 25 = 100
• New average = 25 * 1.2 = 30
• Sum of age including head = 5 * 30 = 150
• Age of the Head = 50
5

6. Average Speed – Type I
A man divides his total route of journey into three equal parts
and decide to travel the three parts with
speed of 15 km/h. 10 km/h and 5 km/ h respectively.
Find his average speed of during journey.
a)2.28 km/h b)9 km/h c)14 km/h d)8.18 km /h
If three equal distances are covered at different spees of A, B
and C km/h, respectively, then average speed during whole
journey =
3ABC
AB+BC+CA
km/h
=
3∗15∗10∗5
150+ 50+75
= 8.18 Km/h 6

7. Average Speed – Type II
A person covers 9 km with a speed of 3 km/h, 25 km with a
speed of 5 km/h and 30 km with a speed of 10 km/h.
Find out the average speed of person.
a)5
9
11
km/h b)11
5
9
km/h c)9
5
11
km/h d)5
5
11
km/h
Let P,Q,R be distances travelled and x,y,z be speeds
Average speed =
P+Q+R
𝑃
𝑥
+
𝑄
𝑦
+
𝑅
𝑧
=
9+25+30
3+5+3
=
64
11
=5
9
11
km/h 7

8. Average Weight
Average weight of three boys P, T and R is 541/3 kg, while the
average weight of three boys T, F and G is 53 kg.
What is the average weight of P, T, R, F and G ?
a)53.8 kg b)52.4 kg c)53.4 kg d)Cannot be determined
(P + T + R) / 3 = 541/3
P + T + R = (163/3) x 3
P + T + R = 163 ............(i)
(T + F + G)/3 = 53
T + G + F = 159 ..........(ii)
Cannot be determined
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9. Average
Weight
The average weight of 4
men, A, B, C and D is 67 kg.
The 5th man E is included
and the average weight
decreases by 2 kg.
A is replaced by F.
The weight of F is 4 kg more
than E .
Average weight decreases
because of the replacement
of A and now the average
weight is 64 kg.
Find the weight of A.
A)78 kgB)66 kg
C)75 kgD)58 kg
9
Sum of the weight of A, B, C and D
= 67 x 4 = 268 kg
and average weight of A, B , C , D and E
= 67 - 2 = 65kg
∴ Sum of the weight of A, B, C, D and E
= 65 x 5 = 325 kg
∴ Weight of E = 325 - 268 = 57 kg
∴ Weight of F = 57 + 4 = 61 kg
average weight of F, B, C, D and E = 64 kg
∴ Sum of the weight of F, B, C, D and E
= 64 x 5 = 320 Kg
∴ Sum of the weights of B, C and D
= 320 - 57 - 61 = 202 kg. Hence A is 66 kg

10. Total
Nine friends have dinner in a hostel.
Eight of them spent ₹ 12 each on their meals and the ninth
spent ₹ 16 more than the average expenditure of all the nine.
Find out the total money spent by them ?
a)₹ 126 b)₹ 135 c)₹ 111 d)₹ 141
Let average expenditure of 9 persons = x.
According to the question,
12 x 8 + (x + 16) = 9x
112 = 8x
X = 14
Total money spent = 9x
= ₹126
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