INFANT JESUS GROUP OF ENGINEERING COLLEGES
PLACEMENT TRAINING – QUANTITATIVE APTITUDE
AVERAGES
IMPORTANT RESULTS:
1) Average is the sum of the values divided by the number of values.
2) If each value is increased / decreased by a constant then the average will also be
increased / decreased by the same constant.
3) If each value is multiplied / divided by a constant then the average will also be multiplied
/ divided by the same constant.
4) The average of any finite sequence of constantly increasing or decreasing numbers will
be half the sum of first and last numbers.
5) If the average of n values is A and a new value N is given then the average of the n  1
NA
values is A 
.
n 1
6) If the average of n values is A and one value B is changed to C then the new average is
CB
A
.
n
7) If the average of n values is A and the average of m other values is B then the average of
(n  A)  (m  B)
m  ( B  A)
the n  m values is
or A 
.
nm
nm
8) If the average of n values is A and after adding a new value if the average of the n  1
values is B then the newly added value is A  (n  1)( B  A) .
1. The average of all the numbers between 6 and 34, which are divisible by 5 is
a) 18
b) 20
c) 14
d) 30
e) none of these
ANSWER: b) 20
SOLUTION: The first number is 10.
The last number is 30
The average is
= 20
2. The average of first five multiples of 3 is
a) 3
b) 9
c) 12
d) 15
e) none
ANSWER: b) 9
SOLUTION: The first multiple of 3 is 3 and the fifth multiple of 3 is 15.
The average of constantly increasing or decreasing values will be half the sum of first and
last number.
The average is
=9
3. If the average of 20 numbers is zero, then at the most, how many of them may be greater than
zero?
a) 0
b) 1
c) 10
d) 19
e) none of these
ANSWER: d) 19
SOLUTION: It is enough if one number is the negative of the sum of the remaining
nineteen positive numbers.
4. The average of three whole numbers is 18. The smallest number is one-third of the largest
number. The middle number is twice the smallest number. Find out the middle number.
a) 18
b) 28
c) 27
d) Data inadequate e) none of these
ANSWER: a) 18
SOLUTION: Sum of the 3 numbers  3  18  54.
s  3l , m  2 s  s : m : l  1 : 2 : 3  k : 2k : 3k  6k  54  k  9  m  2k  18 .
5. The average of 3 numbers is 7 and the average of the first two numbers is 5. What is the
third number?
a) 11
b) 7
c) 3
d) 2
e) 6
ANSWER: a) 11
SOLUTION: sum of the three numbers is 3  7  21.
Sum of the first two numbers is 2  5  10.
Third number = sum of the three numbers – sum of the first two numbers 21  10  11.
6. A motorist completed the journey between A and B at a constant speed of 20Kmph and
covered the return journey from B to A at a constant speed of 30 Kmph. What was the
average speed?
a) 54 Kmph b) 25 Kmph c) 14 Kmph d) 26 Kmph e) none of these
ANSWER: e) none of these
s
; time taken from B to
20
s
2s
2  20  30
A 
; Average speed = distance traveled / time taken =

 24
s
s
30
20  30

20 30
SOLUTION: distance traveled = 2s; time taken from A to B 
7. The average of first nine prime numbers is
1
a) 9
b) 11
c) 11
9
ANSWER: c) 11
d) 11
2
9
e) none of these
1
9
SOLUTION: The first nine prime numbers are 2,3,5,7,11,13,17,19,23.
Average 
100
1
 11 .
9
9
8. The average of 11 results is 60. If the average of first six results is 58 and that of the last six
is 63, find the sixth result.
a) 66
b) 60
c) 64
d) 55
e) none of these
ANSWER: a) 66
SOLUTION: sixth number = (sum of the first 6 numbers + sum of the last six numbers) –
sum of
the 11 numbers  (6  58  6  63)  11  60  6(58  63  110)  6  11.
ALITER :60 + 6 × (58 − 60) + 6 × (63 − 60) = 60 − 12 + 18 = 66.
9. The average age of a class of 39 students is 15 years. If the age of the teacher is included,
then the average increases by 3 months. Find the age of the teacher.
a) 20
b) 24
c) 25
d) 60
e) none of these
ANSWER: c) 25
SOLUTION: If the average of n values is A and after adding a new value if the average
1
of the n  1 values is B then the newly added value is A  (n  1)( B  A) ; 15  40  .
4
10. Of the three numbers second is twice the first and is also thrice the third. If the average of
the three numbers is 44, find the largest number.
a) 48
b) 72
c) 60
d) 90
e) none of these
ANSWER: b) 72
SOLUTION: the numbers are in the ratio
1 1
: 1 :  3 : 6 : 2  3k  6k  2k  3  44  k  12  6k  72.
2 3
11. Find the average of first forty natural numbers.
a) 20
b) 40
c) 20.5
d) 21.5
e) none of these
ANSWER: c) 20.5
SOLUTION: The average of any sequence of constantly increasing or decreasing
numbers will be half the sum of the first and last numbers.
12. Find the average of first twenty multiples of 7.
a) 70
b) 74
c) 74.5
d) 73.5
e) none of these
ANSWER: d) 73.5
SOLUTION: The average of any sequence of constantly increasing or decreasing
7(1  20)
numbers will be half the sum of the first and last numbers. =
 7  10.5
2
13. A library has an average of 510 visitors on Sunday and 240 on other days. The average
number of visitors per day in the month of thirty days beginning with a Sunday is
a) 250
b) 276
c) 280
d) 285
e) none of these
ANSWER: d) 285
SOLUTION: There will be 5 Sundays. If the average of n values is A and the average of
(n  A)  (m  B)
m other values is B then the average of the n  m values is
or
nm
m  ( B  A)
A
.
nm
Average 
5  510  25  240
5  (510  240)
or 240 
 240  45
30
30
14. The average of 5 numbers is 270. If one number is excluded the average becomes 250. The
excluded number is
a) 150
b) 250
c) 350
d) 450
e) none of these
ANSWER: c) 350
SOLUTION: If the average of n values is A and after adding a new value if the average
of the n  1 values is B then the newly added value is A  (n  1)( B  A) .
250  (5  20). = 250 + 100 =350
15. Last year the average salary of 24 employees in a factory was Rs.800. This year 10 of them
gets promoted and their salary increased at an average of Rs.24. What is the average of all
the employees now?
a) Rs.810
b) Rs.500
c) Rs.700
d) Rs.600
e) none of these
ANSWER: a) 810
SOLUTION: If the average of n values is A and the average of m other values is B then
(n  A)  (m  B)
m  ( B  A)
10  24
the average of the n  m values is
or A 
. 800 
nm
nm
24
16. There are 5 numbers. The average of first four is 8 and the last four is 10. If the first number
is 4, what is the last number?
a) 20
b) 18
c) 12
d) 10
e) none of these
ANSWER: c) 12
SOLUTION: sum of the last 4 numbers  4  10  40. Sum of the five numbers
40  4  44.
Sum of the first 4 numbers  4  8  32. Last number  44  32.
17. There are 7 numbers. The average of first six is 9 and the average of last six is 10. If the last
number is 11. What is the first number?
a) 2
b) 5
c) 4
d) 7
e) none of these
ANSWER: b) 5
SOLUTION: sum of the first 6 numbers  6  9  54.
Sum of the five numbers  54  11  65.
Sum of the last 6 numbers  6  10  60.
First number  65  60.
18. There are 4 numbers whose total is 26. The average of the first three numbers is 5 and the
average of the last three is 7. If the second number is 9, what is the third number?
a) 2
b) 3
c) 4
d) 1
e) none of these
ANSWER: d) 1
SOLUTION: The sum of the first 3 numbers  3  5  15 .
The sum of the last 3 numbers  3  7  21.
The sum of all the 4 numbers is 26.
The sum of the second and third numbers = 15  21  26  10. The third number is
10  9  1.
19. 80 Kg of sugar at Rs.7 per kilo and 120 Kg of sugar at Rs.6 per kilo were bought. What is
the average cost of both?
a) Rs.3.70
b) Rs.4.50
c) Rs.6.40
d) Rs.5
e) none
ANSWER: c) Rs.6.40
SOLUTION: If the average of n values is A and the average of m other values is B then
(n  A)  (m  B)
m  ( B  A)
80  1
the average of the n  m values is
or A 
. 6
nm
nm
200
20. A batsman’s average was 20 runs. In another 2 innings he scored 0 and 10 runs and his
average became 15 runs. How many innings did he play.
a) 2
b) 3
c) 4
d) 6
e) none of these
ANSWER: C) 4
SOLUTION: It is better to proceed from the answers. The original average 20 decreases
to 15 while the average in 2 innings is only 5 implies the number of innings already
(4  20)  0  10
played will be more. Hence try 4.
 15 .
6
ALITER:( × 20) + 0 + 10 = ( + 2) × 15; 5 = 30 − 10 = 20;
21. The average age of 36 students is 14 years. When the teacher’s age is included to it, the
average increases by 1. What is the teacher’s age?
a) 31
b) 36
c) 51
d) cannot determine e) none of these
ANSWER: c) 51
SOLUTION: If the average of n values is A and after adding a new value if the average
of the n  1 values is B then the newly added value is A  (n  1)( B  A) . 14  (37  1)
22. The average monthly salary of 20 employees in an organization is Rs.1500. If the manager’s
salary is added, then the average salary increases by Rs.100. What is the manager’s monthly
salary?
a) 2000
b) 2400
c) 3600
d) 4800
e) none of these
ANSWER: c) 3600
SOLUTION:
If the average of n values is A and after adding a new value if the average of the n  1
values is B then the newly added value is A  (n  1)( B  A) . 1500  (21 100) =1500 +
2100 = 3600
23. The average price of 3 items of furniture is Rs.15, 000. If their prices are in the ratio 3 : 5 : 7,
the price of the cheapest item is:
a) Rs.9,000 b) Rs.15,000 c) Rs.18,000 d) Rs.21,000 e) none of these
ANSWER: a) Rs.9, 000
SOLUTION: Prices be 3k, 5k and 7k. 3k  5k  7 k  3  15000  k  3000;3k  9000.
24. The average age of boys in a class of 20 students is 20.1 years. What will be the average age
if 5 new students whose average age is 20.9 join it?
a) 20.5
b) 21.5
c) 22.5
d) 20.26
e) none of these
ANSWER: d) 20.26
SOLUTION: If the average of n values is A and the average of m other values is B then
(n  A)  (m  B)
m  ( B  A)
5  0.8
the average of the n  m values is
or A 
. 20.1 
nm
nm
25
==
25. The average age of 3 boys is 32 years. If their age are in the ratio 3 : 5 : 8, the age of the
youngest boy is
a) 5 years
b) 6 years
c) 7 years
c) 4 years
e) none of these
ANSWER: e) none of these
SOLUTION: 3k  5k  8k  3  32  k  6;3k  18
26.
The average mark of 50 students is 43. It was decided that each student be given one
grace mark. What will be the new average?
a) 39
b) 43.5
c) 44
d) 50
e) none of these
ANSWER: c) 44
SOLUTION: If each value is increased / decreased by a constant then the average will
also be increased / decreased by the same constant.
27.
The average of 15 numbers is 27. If 3 is added to every number, find the new average.
a) 32
b) 30
c) 31.5
d) 72
e) none of these
ANSWER: b) 30
SOLUTION: If each value is increased / decreased by a constant then the average will
also be increased / decreased by the same constant.
28.
The average salary of all the workers in a workshop is Rs.8,000. The average salary of 7
technicians is Rs.12,000 and the average salary of the rest is Rs.6,000. The total number
of workers in the workshop is
a) 20
b) 21
c) 22
d) 23
e) none of these
ANSWER: b) 21
SOLUTION: If the average of n values is A and the average of m other values is B then
(n  A)  (m  B)
m  ( B  A)
the average of the n  m values is
or A 
.
nm
nm
6000 
7  (12000  6000)
 8000  7  6000  n  2000
n
29
In a school with 600 students, the average age of the boys is 12 years and that of the girls
is 11 years. If the average age of the school is 11 years 9 months then the number of girls
in the school is
a) 250
b) 270
c) 300
d) 350 e) none of these
ANSWER: e) none of these
SOLUTION: Let n be the number of girls in the class. If the average of n values is A and
the average of m other values is B then the average of the n  m values is
(n  A)  (m  B)
m  ( B  A)
n
3
1
or A 
. Hence 12 
 11  n  600   150.
nm
nm
600
4
4
30. The average age of 35 students in a class is 16 years. The average age of 21 students is 14.
What is the average age of remaining 14 students?
a) 15
b) 17
c) 18
d) 19
e) none of these
ANSWER: d) 19
SOLUTION:
(35  16)  (21  14)
 40  21
14
31. The average of ten numbers is 7. If each number is multiplied by 12, then the average of the
new set of numbers is :
a) 7
b) 19
c) 82
d) 84
e) none of these
ANSWER: d) 84
SOLUTION: If each value is multiplied / divided by a constant then the average will also
be multiplied / divided by the same constant.
32. The mean of 50 observations was 36. It was later found that an observation 48 was wrongly
taken as 23. The corrected new mean is
a) 35.2 b) 36.1
c) 36.5 d) 39.1
e) none of these
ANSWER: c) 36.5
SOLUTION: If the average of n values is A and one value B is changed to C then the
CB
48  23
new average is A 
= 36 
n
50
33. The average weight of A, B and C is 45 Kg. If the average weight of A and B is 40 Kg. and
that of B and C is 43 Kg, then the weight of B is
a) 17 Kg.
b) 20 Kg.
c) 26 Kg.
d) 31 Kg.
e) none of these
ANSWER: d) 31kg.
SOLUTION: weight of B = (weight of A + weight of B) + (weight of B + weight of C)(Weight of A + weight of B + weight of C)
= (2  40)  (2  43)  (3  45)
=80 + 86 – 135 = 31
34. The average age of husband, wife and their child 3 years ago was 27 years and that of wife
and child five years ago was 20 years. The present age of husband is
a) 35 years
b) 40 years
c) 50 years
d) 45 years
e) none of these
ANSWER: b) 40 years
SOLUTION: h  w  c 3 years ago was 3  27  81.
w  c 3 years ago was 2  (20  2)  2  22  44.
3 years ago h  81  44  37.
35. The average height of 25 boys is 1.4 meters. When 5 boys leave the group, then the average
height increases by 0.15m. What is the average height of the 5 boys who leave?
a) 0.8m
b) 0.9m
c) 0.95m
d) 1.05m
e) none of these
ANSWER: a) 0.8m
SOLUTION:
25  1.4  20  1.55
 7  4  2.2 = 3 – 2.2 = 0.8
5
36. In a shopping mall with a staff of 5 members the average age is 45 years. After 5 years a
person joined them and the average age is again 45 years. What is the age of the 6th
person?
a) 25
b)20
c)45
d)30
ANSWER: b) 20
SOLUTION: Average age of the 5 persons after 5 years is 50.
37. If the average of n values is A and after adding a new value if the average of the n  1 values
is B then the newly added value is A  (n  1)( B  A) .
Age of the sixth person  50  6(50  45) = 50 – (6 X 5) = 50 – 30 =20.
38. There are 4 men in a group. The average age of the four before 4 yearswas 45. One man is
added to the group now and his age is 49. What is the average age of all the 5 men now?
a) 43
b)45
c)47
d)49
ANSWER: d) 49
SOLUTION: The average age of the 4 men now is 49.
Age of the fifth man now is also 49.
(4  49)  49
Averageage of 5 men 
.
5
39. 6 persons are in different age groups. After two years their average age will be 43. A seventh
person joins with them and the current average age has become 45. Find the age of seventh
person.
a) 43
b)69
c)52
d)31
ANSWER: b) 69
SOLUTION: Average age of 6 persons now is 41.
If the average of n values is A and after adding a new value if the average of the n  1
values is B then the newly added value is A  (n  1)( B  A) .
Age of the seventh person is 41  (7  4)
40. The average age of four men before 2 years is 55. Now one man of age 45 joins them.
What is the average age of all?
a) 55
b) 54.5
c) 54.6
d) 54.7
ANSWER: c) 54.6
SOLUTION: Average age of 4 men now is 57.
If the average of n values is A and a new value N is given then the average B of the n  1
NA
values is A 
.
n 1
Average age of all 5 men = 57 
12
 57  2.4 = 54.6
5
41. The average age of 8 persons in a committee is increased by 2 years when two men aged 35
years and 45 years are substituted by two women. Find the average age of the two women.
a) 48
b) 45
c) 51
d)42
ANSWER: a) 48
SOLUTION: Increase in average =
w1  w2  80  2    96 
w1 w2
8
w w
1
2
2
 48.