AVERAGE
1. The average of first five multiples of 3 is :
Ans: 9
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
1,2,3 ,….. n
n 1
If n is odd, the formula is th term
2
Answer with Explanation:
The five multiples of 3 is 3, 6, 9, 12, 15
n 1 5 1
th term
2 2
rd
6/2 th term = 3 term
Here 3rd term is 9
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2. A student was asked to find the arithmetic mean of the numbers 3, 11, 7, 9, 15,
13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What should be the
number in the place of x ?
a. 3 b. 7 c. 17 d. 31
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
The formula for arithmetic mean is x = x
N
Answer with Explanation:
Given that x = x
N
Here N =12 and x = 12
x = x
N
137 x
12 =
12
144 = 137 + x
144 - ,137 = x
7=x
X=7
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3. A library has an average of 510 visitors on Sundays and 240 on other days. The
average number of visitors per day in month of 30 days beginning with a Sunday
is:
a. 250 b. 276 c. 280 d.285
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Sundays : 1, 8, 15, 22, 29 = 510 x 5 = 2550
= 240 x 25 = 6000
= 8550
the month of 30 days
8550 / 30 = 285
Average visitors per day = 285
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4. The average of 50 numbers is 30. If two numbers, 35 and 40 are discarded, then
the average of the remaining numbers is nearly:
a. 28.32 b. 29.68 c. 28.78 d. 29.27
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Total sum of 48 numbers = (50x30 – (35 +40)
= 1500 – 75
= 1425
Average = 1425 / 48 = 29.68
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5. The average score of a cricketer for ten matches is 38.9 runs. If the average for
the first six matches is 42, then find the average for the last four matches.
a. 33.25 b. 33.5 c. 34.25 d. 35
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Total sum of last 4 matches = (10 x 38.9) – (6 x 42)
= 389 – 252 = 137
Average = 137 / 4 = 34.25
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6. The average price of 10 books is Rs.12 while the average price of 8 of these
books is Rs.11.75. Of the remaining two books, if the price of one book is 60%
more than the price of the other, what is the price of each of these two books?
a. Rs.5, Rs.7.50 b. Rs.8, Rs.12 c. Rs.10, Rs.16 d. Rs.12, Rs.14
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Total cost of 10 books = 120
Total cost of 8 books = 94 (-)
The cost of 2 books = 26
x + y = 26 -------(1)
Given that the price of 1 book is 60% more than the other price
160
y + y = 26
100
160
Y( +1) = 26
100
26x100
y=
260
Y = 10
Substituting Y = 10 in (1) we get,
X + 10 = 26
X = 16
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7. Of the three numbers, the first is twice the second and the second is twice the
7
third. The average of the reciprocal of the numbers is . The numbers are:
72
a. 16, 8, 4 b. 20, 10, 5 c. 24, 12, 6 d. 36, 18, 9
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Let three numbers be x, y,z
Given x = 2y x = 4z ; y = 2z ; z = z
The average of reciprocal numbers is 7/72
1 1 1
x y z
= 7/72
3
yz xz xy 2 z 2 4 z 2 8z 2
= 7/72 = 7/72
3 xyz 3x 4 zx 2 zxz
14 z 2 7
= 7/72 = 7/72
24 z 3 12 z
504 = 84z
Z = 504/84 = 6
x = 4 x6 = 24
Y = 2 x 6 = 12
Answer = x = 24, y = 12 ; z= 6
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8. Average of ten positive numbers is x . If each number by 10%, then x :
a. remains unchanged b. may decrease c. may increase
d. is increased by 10%
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Ten +ve numbers in x is
10 10 10 10 10 10...10
= x
10
x = 10
It is increased by 10%.
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1
9. The average weight of three boys A, B and C is 54 kg, while the average
3
weight of three boys B, D and E is 53 kg. What is the average weight of A, B, C, D
and E?
a. 52.4 kg b. 53.2 kg c. 53.8 kg d. Data inadequate
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
In this sum, one data is missing
There fore The answer is Data inadequate.
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10. The average age of 36 students in a group is 14 years. When teacher’s age is
included to it, the average increases by one. What is the teacher’s age in years?
a. 31 b. 36 c. 51 d. None of these
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
The average age 36 students = 14
37 members = 14 +1 = 15
The teacher’s age = (37 x 15 – (36x14)
= 555 – 504 = 51
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11. A cricketer has a certain average for 10 innings. In the eleventh inning, he
scored 108 runs, there by increasing his average by 6 runs. His new average is:
a. 48 runs b. 52 runs c. 55 runs d. 60 runs
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Let the average for d10 innings be x
10 x 108
Then =x+6
11
10x +108 = 11x +99
108 – 66 = -10x +11x
X = 42
The new average = x+6
= 42 + 6
= 48 runs.
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12. 10 years ago, the average age of a family of 4 members was 24 years. Tow
children having been born (with age difference of 2 years), the present average age
of the family is the same. The present age of the youngest child is:
a. 1 year b. 2 years c. 3 years d. 5 years
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
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13. The average salary of all the workers in a workshop is Rs.8000. The average
salary of 7 technicians is Rs.12000 and the average salary of the rest is Rs.6000.
The total number of workers in the workshop is:
a. 20 b. 21 c. 22 d. 23
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Let the total number of workers in the workshop = x
Given Average of all workers = 8000 8000x
Average of 7 members = 12000 7 x 12000 = 84000
Average of remaining workers = 6000 6000 X (x – 7) 6000x – 42000
Find out the total number of workers
8000x = 84000 + 6000x – 42000
2000x = 42000
X = 21
There fore the total number of workers in the workshop is = 21.
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14. In an examination, a pupil’s average marks were 63 per paper. If he had
obtained 20 more marks for his geography paper and 2 more marks for his
History paper, his average per paper would have been 65. How many papers
was therein the examination? Answer is 11
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Let the number of papers = x
Average of x papers = 63
Then total mark = 63 x X
Given he obtained 20 more in geography and 2 more marks in History
The new average is = 65
To find out the number of papers = 63x + 20 + 2 = 65x
= 22 = 2x
X = 11
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15. The average age of students of a class is 15.8 years. The average age of
boys in the class is 16.4 years and that of the girls is 15.4 years. The ratio of the
number of boys to the number of girls in the class is:
a. 1 : 2 b. 2 : 3 c. 3 : 4
d. 3 : 5
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Let the ratio be K : 1
Kx16.4 + 1x 15.4 = (K+1) x 15.8
(16.4 – 15.8 )k = (15.8 – 15.4)
0.6k = 0.4
K = 0.4/0.6 = 2/3
The required ratio = 2/3 :1
= 2:3
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16. What is the average salary of 15 employees?
I. Average salary of 7 clerical cadre (out of the 15 employees) is Rs.8500.
II. Average salary of 5 officer cadre (out of the 15 employees) is Rs.10000.
III. Average salary of the 3 sub-staff employees (out of 15 employees) is Rs.2500.
a. None b. I only c. II only d. III only
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
All the three statements should be added and then only the average salary of 15
staffs we can get. So, a) None is the answer.
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17. The average of all odd numbers up to 100 is :
Answer : 50
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
1,2,3 ,….. n
n 1
If n is odd, the formula is th term
2
Answer with Explanation:
The average of all odd numbers up to 100 is 1+3+5+7+9+…+99
There fore here n = 99
99 1
= 100/2 = 50
2
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18. The average of 7 consecutive numbers is 33. The largest of these number is :
Answer:36
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Let the numbers x, x+1, x+2, x+3, x+4, x+5, x+6
Answer with Explanation:
x, x 1, x 2, x 3, x 4, x 5, x 6
Given = 33
7
7 x 21
= 33
7
7x +21 = 33x7
7x + 21 = 231
7x = 231 – 21 = 210
X = 210/7 = 30
There for the largest number is x +6 = 30+6 = 36.
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19. The average of four consecutive even numbers is 27. The largest of these
number is :
Answer: 30
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Let the numbers x, x+2, x+4, x+6
Answer with Explanation:
x, x 2, x 4, x 6
Given = 27
4
4 x 12
= 27
4
4x +12 = 27 x 4
4x + 12 = 108
4x = 108 – 12 = 96
X = 96/4 = 24
There for the largest number is x +6 = 24+6 = 30.
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20. The average height of 30 boys out of a class of 50, is 160cm, if the average
height of the remaining boys is 165cm, the average height of the whole class (in
cm) is :
Answer:162
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Given the average of 30 boys is 160 cm.
Total 50
The remaining ( 50-30 = 20)
The average of 20 boys is 165 cm
(30 x160) (20 x165)
The required average =
50
4800 3300
= 8100/50 = 162 cm
50
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21. The average of tow numbers is M. If one is N, then the other number is :
Answer : 2M-N
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
We assume that the other number is x
The one number is N
The average of two numbers is M
X N
=M
2
X+N = 2M
X = 2M – N
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22. The average of 5 results is 46 and that of the first 4 is 45. The fifth result is :
Answer: 50
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Given average of 5 results = 46
Average of first 4 result = 45
Fifth result = (5x46) (4 x45)
= 230 – 180 = 50
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23. The average of three numbers is 20. If two numbers are 16 and 22 the third
number is :
Answer: 22
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Given that the average of three number is 20
We assume the three numbers are x, y, z
The two number are given, we take x = 16 and y = 22
The average of three numbers is 20
x yz
= 20
3
16 22 z
= 20 16 + 22 + z = 20 x 3
3
Z = 60 - 38 22
The third number is 22.
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24. The average of eight numbers is 14. The average of six of these numbers is 16.
The average of remaining two numbers is :
Answer: 8
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
The total sum of remaining two = (8x14 ) – (6x16)
= 112 – 96
= 16
the average of these two numbers = 16/2 = 8
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25. The average of ten numbers is 7. If each number is multiplied by 12, then the
average of new set of numbers is:
Answer: 84
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
The average of new set is 12 x 7 = 84.
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26. A class has two sections, in one of which there are 40 students with an average
of 14.5 years. The average of the class is 14.2 years. If there be 32 students in the
other section, its average age is :
Answer: 13.825
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Given 40 students average 14.5 years
(40 + 32) = 72 students average 14.2 years
The total age of 32 students = (72 X 14.2 – 40 x 14.5) years
= (1022.4 – 580) years
= 442.4 years
The average = 442.4/32 = 13.825 years.
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27. The average of 50 numbers is 38, if two numbers, namely 45 and 55 are
discarded, the average of the remaining number is :
Answer: 37.5
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
The total sum of 48 numbers
= [(50x38) – (45 +55)]
= 1900 – 100
= 1800
Average = 1800/48 = 37.5
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28. The mean of 100 observations was calculated as 40. It was found later on that
one of the observations was misread as 83 instead of 53. The correct mean is :
Answer: 39.7
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Given mean of 100 = 40
One is 53-83 = -30
Correct sum = (40 x 100 ) + (53-83)
= 4000-30
= 3970
Correct mean = 3970 / 100 = 39.7
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29. The average of six numbers is 30. If the average of first four is 25 and that of
last three is 35, the fourth number is :
Answer: 25
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Given average of 6 numbers = 30
Average of first 4 is = 25
Average of last 3 is = 35
The fourth number is = (4x25 ) + (3x35) – (6x30)
= 100 + 105 – 180
= 205 – 180 = 25
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30. In seven given numbers, the average of first four numbers is 4 and that of the
last four numbers is also 4. If the average of these seven numbers is 3, the fourth
numbers is:
Answer: 11
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Given average of first 4 numbers = 4
Average of last 4 numbers = 4
Average of 7 numbers = 3
The fourth number = (4x4) +(4x4) – (7x3) = 16 + 16 – 21
= 32 – 21 = 11
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31. The average of 25 results is 18. The average of first twelve of them is 14 and
that of last twelve is 18, the thirteenth result is : Answer: 78
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Given Average of 25 results = 18
Average of first 12 result = 14
Average of last 12 result = 18
The thirteenth result = (25x18) – {(12x14) + (12x17)}
= 450 – (168 + 204)
= 450- 372 = 78
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32. Out of four numbers, the average of first three is 16 and that of the last three is
15, If, the last number is 18, the first number is:
Answer: 21
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Given average of first three = 16
Average of last three = 15
And last number = 18
Sum of 2nd and 3rd number = (3x 15) – 18
= 45 – 18
= 27
The first number = (3 x 16 ) – 27
= 48 – 27
= 21
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33. Mukesh has twice as much money as Sohan and Sohan has 50% more money
than kwhat Pankaj has. If the average money with them is Rs.110, then Mukesh
has:
Answer: 180
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Suppose Pankaj has Rs. X
Then, Sohan has 150% of Rs. X
= Rs . 3x
150
xX = Rs.
100 2
Then Mukesh has Rs. 3x
x + 3x/2 + 3x = (110 x3)
2x + 3x + 6x = 660
11x = 660
x = 660/11 = 60
Mukesh has Rs. 3 x 60 = Rs. 180
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34.A motorist travels to a place 150 km away at an average speed of 50 km per
hour and returns at 30 km per hour. His average speed for the whole journey in km
per hour is:
Answer: 37.5
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
2 xy
Average Speed = km/hr
x y
Answer with Explanation:
Given x = 50, y = 30
2 xy
Average Speed = km/hr
x y
2 x50 x30
= km / hr
50 30
= 3000/80
= 37.5 km / hr
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35. The average of 30 students is 9 years. If the age of their teacher is included, it
becomes 10 years. The ago of the teacher (in years) is :
Answer: 40
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Given average of 30 students = 9 years
Average of 31 members = 10 years
The age of teacher = (31 x 10) – (30 x 9)
= 310 – 270
= 40 years
Another Method:
The age of the teacher = 10 + (10-9) (30)
= 10 + (1) (30)
= 10 + 30
= 40 years.
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36. The average weight of 50 balls is 2 lbs. If the weight of the container be
included, the average weight will increase by 0.05 lbs. The weight of the container
is :
Answer: 4.55
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Given average weight of 50 balls = 2 lbs
Included container average is (50+1) = increase of 0.05
= 2.05 lbs
The weight of the container is = 51 x 2.05 – 50 x 2
= 104.55 – 100
= 4.55 lbs
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37. The average salary per month of 30 employees in a company is Rs.4000. If the
manager’s salary is added, the average salary increase to Rs.4300. What is the
salary os the manager?
Answer:77
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Given average salary of 30 members = 4000/-
Added one member salary (30 + 1) = 4300/-
The salary of the manager is = (31 x 4300) – (30 x 4000)
= 133300 – 120000
= 13300/-
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38. The average weight of 8 men is increased by 1.5 kg when one of the men who
weight 65 kg is replaced by a new man. The weight of the new man is :
Answer:77
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Total weight increased = (8 x 1.5) kg
= 12 kg
The weight of new man = (65 + 12 ) kg
= 77 kg.
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39. The average of five consecutive odd numbers is 61. What is the difference
between the highest and lowest numbers?
Answer: 8
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Let the numbers be
X, x+2, x + 4, x + 6, x + 8
Given average is 61
X, x 2, x 4, x 6, x 8
= 61
5
5 x 20
= 61
5
5x + 20 = 305
5x = 305 – 20 = 285
X = 57
The highest number = x + 8 = 65
Lower number = x = 57
The difference is 65 – 57 = 8
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40. 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?
Answer: 30 years
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
(P + Q) , 5 years ago = (15 x 2) = 30 years
(P+Q), now = [30 + (5x2)] = 30 + 10 = 40 years.
(P + Q + R), now = (20 x 3) = 60 years
R, now = (60 - 40) years
= 20 years
R, after 10 years = (20 +10) years
= 30 years
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41. Three years ago, the average age of a family of 5 members was 17 years. A
baby having been born, the average age of the family is the same today. The
present age of the baby is :
Answer: 2 years
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Total age of 5 members, 3 years ago = (17 x 5) = 85 years
Total age of 5 members, now = [ 85 + (3x5)]
= 85 + 15 = 100 years
Total age of 6 members now = (17 x 6) = 102 years
The age of the baby = (102 – 100) = 2 years.
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42. The average marks obtained by 22 candidates in an examination is 45.
The average of the first ten is 55 while that of the last eleven is 40. The
marks obtained by the 11 candidates are
a) 0 b) 3 c) 4 d) None of these
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Given Average of 22 students = 45
Average of first ten = 55
Average of last ten = 40
The marks obtained by 11 candidates are
= (22 x 45) – { (55 x 10) + (40 x 11)}
= 990 – (550 + 440)
= 990 – 990 = 0
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43. The average weight of 8 persons is increased by 2.5 Kg. When one of
them, whose weight is 56 kg is replaced by a new man. The weight of the
new man is
a) 64 kg b) 76 kg c) 80 kg d)None of these
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
Total weight increased = 8 x 2.5
= 20 kg
Weight of new man = 56 + 20
= 76 kg.
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44. The average age of group of 10 students is 15 years. When 5 more
students joined the average age rose by 1 year. The average age (in years) of
the new student is
a) 18 years b) 17 years c) 16 years d) None of these
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
The average of 10 students = 15 15 x 10 = 150
When 5 more students added, the average is = 16 16 x 15 = 240
The average age of new student is = 240 – 160 = 90
= 90/5 = 18 years
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45. A man spends Rs. 750 on an average during first 8 months. During the
next 4 months he spends Rs. 680 per month. He took loan of Rs. 320 during
the year and paid Rs. 600 for LIC premium. Find his monthly average
income
a) Rs. 650 b) Rs.750 c) Rs. 850 d) Rs.900
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Total Expenditure – Loan taken = Monthly Income
Answer with Explanation:
Expenditure for First 8 months = 6000 (750 x 8)
Expenditure for next 4 months = 2720 (680 x 4)
LIC premium paid = 600
Total Expenditure on a year = 9320.00
Month’s average expenditure = 9320 / 12 = 776.66
Loan taken a year = 320
Months average = 320/12 = 26.66
Monthly average income = 776.66 – 26.66 = 750.00 (Apply above formula)
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46. 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 degrees.
The temperature of the first and fifth days were in the ratio 7:8, then what is the
temperature on the fifth day?
a) 64 degrees b) 62 degrees c) 66 degrees d)
None of these
Difficulty Level : Easy Moderately easy Difficult
Basic Formula:
Answer with Explanation:
First four days average Temperature = 580
1, 2,3, 4 th days total temp. = 58 x 4 = 232
Then 2, 3, 4, 5 days total temp. = 60 x 4 = 240
Let the unknown temp. be x
5th day – 1st day = 240 – 232 = 8 (2, 3, 4 days temp. is common )
Given the ratio of first and fifth day is 7:8
8x – 7x = 8
X=8
Fifth day’s temperature = 8x = 8x8 = 64
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