Average Aptitude Problem Shortcuts, Tricks, Formulas and Solutions.
Average Theory
Average is an indicator of a specified characteristics of a group. The average value is arrived at by distributing equally the total available vale of the group among all the members of the group.
Traditionally, average is calculated by dividing the sum of all the numbers by the number of numbers.
Example, if five articles are bought for Rs.345, Rs.375, Rs.225, Rs.255 and Rs.300. then the average price of the article is
Point to Remember
1) If the toal value of all items in a group of n items is V, then the average per item of the group =
2) The average always lies between the greater and the least of the individual value of the items in the group.
3) For a group of items True average = Assumed Average + Average of Individual deviations from the assumed average.
4) For two groups of items of respective average of P1 and P2 and containing Q1 and Q2 items respectively, the weighted average of the two groups =
Average can also be seen as the central value of all the given values. To facilitate the calculation, the above procedure can be modified and the modified method is called the Method of Deviations.
In this method a number which is between the lowest and the highest values is arbitrarily assumed as the average. Let say we assume 325, the deviation of the individual values are.
(345  325), (375 – 325), (225 – 325), (255 – 325) and (300 325)
Now finding the average of deviations gives us.
Algebraic sum of deviations = 20 + 50 100 – 70 – 25 = 125
Average of deviations =
So, Average = Assumed Central Value + Average of Deviations = (325) + (25) = 300
Change in values and in averages:
1) If the value of each element in a group is increased or decreased by the same value (say k), the average of the group will also correspondingly increase or decrease by the same value i.e. k
2) If the value of each element in a group is either multiplied or divided by the same value say m, the average of the group will also correspondingly get multiplied or divided by the same value i.e. m
Combining two or more groups:
When two or more groups are combined to form a single group, then the average of the newly formed group is called the “Weighted Average of the Groups"
For example, if the average weight of a group of 20 people is 50kg and another group of 30 people has an average weight of 60 kg, then the weighted average of the group (i.e. the average weight of the combined group of 50 people) is:
The same thing can be generalized and algebraically represented as
Where, p is the weighted average, P1 and P2 are the average of the two groups and Q1, Q2 are the respective number of items in the two group.
Solved Questions of Average asked in previous year exams
Example 1
Average age Dharam, Prem and Praan is 84 years. When Amit joins them the average age of Dharam, Prem, Praan and Amit becomes 80 years. A new person Alok, whose age is 4 years more than Amit replace Dharam and the average age of Prem, Praan, Amit and Alok becomes 78 years. What is the age of Dharam?
Solution: Since the average age of Dharam, Prem and Praan = 84 years, so we can assume that the age of Dharam, Prem and Praan is 84 years.
Now
Decrease 4 years in the age of Dharam, Prem and Praan (total = 4 + 4 + 4 = 12) now the average age of Dharam, Prem and Praan = 80 years, so we can assume that the age of Dharam, Prem and Praan is 80 years.
Now decrease in the age of Dharam, Prem and Praan can be attributed to the increase in the age of Amit. So after getting 12 years in total Amit is at 80 years, The original age of Amit = 80 – 12 = 68 Years.
And the age of Alok is 4 years more than Amit,
So Alok’s age is 68 + 4 = 72 years.
Now the average age of Dharam, Prem, Praan and Amit = 80 years
Dharam, Prem, Praan and Amit = (80 + 80 + 80 + 80) = 320
And the average age of Prem, Praan, Amit and Alok = 78 years
So Prem + Praan + Amit + Alok = (78 + 78 + 78 + 78) = 312
Since the average difference between the age of Dharam and Alok is 2 years)
Difference (Dharam – Alok) = 2 * 4 = 8 years
Since Alok = 78 years, so Dharam = 80 years.
By using Central Value Method of average every question of average can be done easily by mental calculation. Just practice few questions and you will be expert in solving Average questions.
Example 2
The average score of Sachin after 25 innings is 46 runs per innings, if after the 26th innings, his average runs increased by 2 runs, then what is the score in the 26th inning ?
Solution: Run in 26th inning = Total runs after 26th innings – Total runs after 25th innings.
= 26 × 48 – 25 × 46 = 98
Alternatively, this question can be done by the above given central value meaning of average. Since the average increase by 2 runs, we can assume that 2 runs have been added to his score in each of the first 25 innings. Now the total runs added in the 26th inning, which must be equal to 25 × 2 = 50 runs.
Hence, runs scored in the 26th inning = new average + old innings × change in average
= 48 + 25 × 2 = 98.
Some Special cases of Average:
Average involving time, speed and distance.
However, while solving the question involving time, speed and distance, we should assume some distance preferably the LCM of all the given speeds.
Example: Sohan Lal goes to Mumbai from Allahabad at a speed of 40km/h and returns with the speed of 60km/h. what is his average speed during the whole journey?
Solution: Assuming that the total distance between Mumbai and Allahabad is 120Km (LCM of 40 and 60) the total time taken (Mumbai – Allahabad and Allahabad – Mumbai) = 3 + 2 = 5h
So, average speed = = 48km/h
Very Important Questions on Average  Must Read
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Question 1 of 38
1. Question
Average marks obtained in History by 45 students in 'A' division are 75 and the average marks obtained by 40 students tn"'B' division are 78. What are the overall average marks obtained in History by the students in both the divisions (rounded off to two digits after decimal?
Correct
Required average =
= = 76.41
Incorrect
Required average =
= = 76.41

Question 2 of 38
2. Question
The average age of Ram, Hari and Gopal is 42yr. If their ages are in the ratio of 2 : 3 : 4 respectively, what is the age of Hari in years?
Correct
Incorrect
Let the ages of Rarn, Hari and Gopal be 2x years, 3x years and 4x years respectively.
therefore = 42
9x = 126
x = 14
the age of Hari = 3x years = 42 years

Question 3 of 38
3. Question
The average age of 60 boys in a class was calculated as 12 yr. It was later realised that the actual age of one of, the boys in the class was 12.5 yr but it was calculated as 14 yr. What is the actual average age of the boys in the
class?Correct
Actual average age =
=
= = 11.975 years
Incorrect
Actual average age =
=
= = 11.975 years

Question 4 of 38
4. Question
The average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighting 65 kg. What might be the weight of the new person?
Correct
Incorrect
The weight of the new person = 65 + 8 2.5
= 65 + 20 = 85 kg

Question 5 of 38
5. Question
The average of 5 consecutive even numbers A, B, C, D and E is 52. What is the product of B and E ?
Correct
Let the five consecutive even numbers A, B, C, D and E
be x, x + 2, x + 4, x + 6 and x + 8, respectively.
now,
5x + 20 = 260
5x = 240
x = 48
Incorrect
Let the five consecutive even numbers A, B, C, D and E
be x, x + 2, x + 4, x + 6 and x + 8, respectively.
now,
5x + 20 = 260
5x = 240
x = 48

Question 6 of 38
6. Question
The average age of five officers in a department is 32 yr. If the age of their supervisor is added the average increased by 1. What is the supervisor's age?
Correct
The supervisor's age = 33 + 5 (33  32) = 33 + 5 = 38 yr
Incorrect
The supervisor's age = 33 + 5 (33  32) = 33 + 5 = 38 yr

Question 7 of 38
7. Question
The average temperature on Tuesday, Wednesday and Thursday was 37 C. The average temperature on Wednesday, Thursday and Friday was 38 C. If the temperature on Friday was 39 C, find the temperature on Tuesday.
Correct
Tuesday + Wednesday + Thursday =
Friday + Wednesday + Thursday =
Friday  Tuesday = 3 (38  37)
39  Tuesday = 3
Tuesday = 36
Temperature,on Tuesday =
Incorrect
Tuesday + Wednesday + Thursday =
Friday + Wednesday + Thursday =
Friday  Tuesday = 3 (38  37)
39  Tuesday = 3
Tuesday = 36
Temperature,on Tuesday =

Question 8 of 38
8. Question
Vibhor obtained 66, 74, 55, 92, 79 (out of 100) in English, Maths, Physics, Chemistry and Biology. what's his average marks ? (sbi 2005)
Correct
So, let's make equation from the given information :
Average =
Average = 73.2%
Incorrect
So, let's make equation from the given information :
Average =
Average = 73.2%

Question 9 of 38
9. Question
In Ashish opinion, his weight is greater than 55 kg but less than 62 kg. His father does not agree with Ashish and he thinks that Ashish weight is greater than 50 kg but less than 60 kg. His sister’s view is that his weight can't be greater than 58 kg. If all of them are correct in their estimation, what is the average of different probable weights of Ashish ? (railway 2004)
Correct
Let Ashish weight X kg.
According to Ashish , 55 < X < 62
According to Ashish father, 50 < X < 60
According to Ashish sister, X < 58
The values satisfying all the above conditions are 56 & 57.
Therefore, Required average =
So, the Ashish weight is 56.5 kg
Incorrect
Let Ashish weight X kg.
According to Ashish , 55 < X < 62
According to Ashish father, 50 < X < 60
According to Ashish sister, X < 58
The values satisfying all the above conditions are 56 & 57.
Therefore, Required average =
So, the Ashish weight is 56.5 kg

Question 10 of 38
10. Question
The average of 15 numbers is zero. Of them, at the most, how many may be greater than zero ? (SBI 2005)
Correct
Average of 15 numbers = 0.
Sum of 15 numbers = (0 15) = 0.It is quite possible that 14 of these numbers may be positive and if their sum is a, then 15th number is (–a).
Incorrect
Average of 15 numbers = 0.
Sum of 15 numbers = (0 15) = 0.It is quite possible that 14 of these numbers may be positive and if their sum is a, then 15th number is (–a).

Question 11 of 38
11. Question
Find the the average of all the numbers between 8 and 55 which are divisible by 7.(SBI 2000)
Correct
Average = = 27 .
Incorrect
Average = = 27 .

Question 12 of 38
12. Question
The average of first seven prime numbers is
Correct
Average = = 8.2
Incorrect
Average = = 8.2

Question 13 of 38
13. Question
A student was asked to find the arithmetic mean of the numbers 4, 11, 7, 9, 16, 13, 8, 19, 18, 21,12 and x. He found the mean to be 12. What should be the number in place of x ?
Correct
Clearly, we have
or 138 +x = 144 or x = 144 – 138 = 6.
Incorrect
Clearly, we have
or 138 +x = 144 or x = 144 – 138 = 6.

Question 14 of 38
14. Question
The average of 5 consecutive numbers is 30. The largest of these numbers is
Correct
Let the number be x, (x+1), (x+2), (x+3) & (x+4).
= 30
5x + 10 = 150, x = , x = 28.
So, the largest number is : x + 4 = 28 + 4 = 32
Incorrect
Let the number be x, (x+1), (x+2), (x+3) & (x+4).
= 30
5x + 10 = 150, x = , x = 28.
So, the largest number is : x + 4 = 28 + 4 = 32

Question 15 of 38
15. Question
A family consists of grandparents, parents and two grandchildren. The average age of the grandparents is 56 years, that of the parents is 27 years and that of the grandchildren is 7 years. What is the average of the family?
Correct
Required Average =\:=\: = 30 years
Incorrect
Required Average = = = 30 years

Question 16 of 38
16. Question
A library has an average of 430 visitors on Sundays and 270 on other days. The around average of the number of visitors per day in a month of 30 days beginning with a Saturday is
Correct
Since the month begins with a Saturday , So there will be five Sundays in the month,
Required Average =
=295.80
So, the around value of visitors per day is 295.
Incorrect
Since the month begins with a Saturday , So there will be five Sundays in the month,
Required Average =
=295.80
So, the around value of visitors per day is 295.

Question 17 of 38
17. Question
If the average marks of three batches of 40, 50 and 60 students respectively is 30, 50 and 70, then the average marks of all the students is
Correct
Required Average = = 61.33
Incorrect
Required Average = = 61.33

Question 18 of 38
18. Question
The average weight of 18 boys in a class is 45.55 kg and that of the remaining 4 boys is 35.25 kg . Find the average weight of all the boys in the class.(SBI 2001)
Correct
Required Average = = 43.67 kg
Incorrect
Required Average = = 43.67 kg

Question 19 of 38
19. Question
A shop of electronie goods is closed on Monday. The average sale per day for the remaining six days of a week is Rs. 15640. If the average sales from Tuesday to Saturday is Rs. 14124, what is the sales on Sunday?
Correct
The Sales on Sunday = 6 15640  5 14124
= (93840  70620)
= Rs. 23220Incorrect
The Sales on Sunday = 6 15640  5 14124
= (93840  70620)
= Rs. 23220 
Question 20 of 38
20. Question
The average of the first 71 natural numbers is(SBI 2003)
Correct
Sum of first n natural numbers =
So, average of first n natural numbers = =
Required average = = 36
Incorrect
Sum of first n natural numbers =
So, average of first n natural numbers = =
Required average = = 36

Question 21 of 38
21. Question
The average of seven consecutive odd numbers is 36. What is the difference between the highest and lowest numbers ?
Correct
Let the numbers be x, x + 2, x + 4, x + 6, x + 8, x + 9, x + 10 & x + 12
then,
= 36
Lowest term = 30, Highest term = 30 + 12 = 42.
⇒ x + 6 = 36 , x = 30. Difference between highest & lowest term = 42 – 30 = 12.
Incorrect
Let the numbers be x, x + 2, x + 4, x + 6, x + 8, x + 9, x + 10 & x + 12
then,
= 36
Lowest term = 30, Highest term = 30 + 12 = 42.
⇒ x + 6 = 36 , x = 30. Difference between highest & lowest term = 42 – 30 = 12.

Question 22 of 38
22. Question
The average of 3, 8, 9 and x is 6 and the average of 17, 2, 5, x and y is 10. What is the value of y ?
Correct
We have = 6
20 + x = 24+
x = 24  20 = 4
similarly = 10
= 10
28 +y = 50
y = 50  28 = 22
Incorrect
We have = 6
20 + x = 24+
x = 24  20 = 4
similarly = 10
= 10
28 +y = 50
y = 50  28 = 22

Question 23 of 38
23. Question
The average of a nonzero number and its square is 7 times the number. The number is
Correct
Let the number be x. then
+x=14x
x(x13) = 0 x = 0 or 13
Incorrect
Let the number be x. then
+x=14x
x(x13) = 0 x = 0 or 13

Question 24 of 38
24. Question
The average age of the boys in a class is 18 years and that of girls is 16 years. The average age for the whole class is :
Correct
Clearly, to find the average, we ought to know the number of boys, girls or students in the class, neither of which has been given.
So, the data provided is inadequate.Incorrect
Clearly, to find the average, we ought to know the number of boys, girls or students in the class, neither of which has been given.
So, the data provided is inadequate. 
Question 25 of 38
25. Question
The average of all natural numbers till 525, is
Correct
We know,
average of all natural numbers till n =
Required average =
Incorrect
We know,
average of all natural numbers till n =
Required average =

Question 26 of 38
26. Question
The body weight of six boys is recorded as 42 kg, 72 kg, 85 kg, 64 kg, 54 kg and 73 kg. What is the average body weight of all the six boys?
Correct
Average weight =
= =65
Incorrect
Average weight =
= =65

Question 27 of 38
27. Question
The average of seven consecutive odd numbers is 47. What is the greatest number among these seven numbers?
Correct
Let the seven consecutive odd numbers be x, x + 2, x + 4, x + 6, x + 8, x + 10, x+12.
therefore,
7x + 42 = 329
7x = 287
x = 41
So, the greatest number = (41 + 12) = 53
Incorrect
Let the seven consecutive odd numbers be x, x + 2, x + 4, x + 6, x + 8, x + 10, x+12.
therefore,
7x + 42 = 329
7x = 287
x = 41
So, the greatest number = (41 + 12) = 53

Question 28 of 38
28. Question
The average age of boys in a class is 12 yr. If the age of Principal is included, the average becomes 13 yr. What is the age of Principal?
Correct
Incorrect
Since, number of students in the class is not given, we cannot calculate the age of principal.

Question 29 of 38
29. Question
The average age of a brother and sister was 35 yr, 5 yr ago. What will be their average age (in years) at present?
Correct
Incorrect
In present situation, their average age = (35 + 5) yr
= 40 yr 
Question 30 of 38
30. Question
The average score of a cricketer in two matches is 27 and in three other matches is 32. Then, find the average score in all the five matches.
Correct
Incorrect
The average score in all the five matches
=
= = = 30

Question 31 of 38
31. Question
The average of first nine prime numbers is
Correct
Incorrect
The average =
= = 11

Question 32 of 38
32. Question
The average of first 20 even numbers is
Correct
Incorrect
The average of first 20 even numbers = (20 + 1)
= 21 
Question 33 of 38
33. Question
Average weight of three boys P, T and R is 54 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, G and H?
Correct
Incorrect
Since, any data about the weight of H is not given, therefore, we cannot calculate the average weight of P, T, R, F, G and H.

Question 34 of 38
34. Question
The average of marks of 14 students was calculated as 71. But it was later found that the marks of one student had been wrongly entered as 42 instead of 56 and of another as 74 instead af 32. The correct average is
Correct
The correct average =
=
= = 69
Incorrect
The correct average =
=
= = 69

Question 35 of 38
35. Question
In a class of 52 students, the number of boys is two less than the number of girls. Average weight of the boys is 42kg, while the average weight of all the 52 students is 40 kg. The average weight of the girls is
Correct
Let the numbers of boys and girls be (x  2) and x, respectively.
x + (x  2) = 52
2x = 54
x = 27
Number of girls = 27  2 = 25
Now, average weight of girls =
=
=
= 38.148 kg
Incorrect
Let the numbers of boys and girls be (x  2) and x, respectively.
x + (x  2) = 52
2x = 54
x = 27
Number of girls = 27  2 = 25
Now, average weight of girls =
=
=
= 38.148 kg

Question 36 of 38
36. Question
The average weights of three groups of girls of 70, 50 and 30 girls are 40 kg, 45 kg and 50 kg, respectively. What is the average weight of all the 150 girls?
Correct
Average weight of all the 150 girls
=
=
= = 43.67 kg
Incorrect
Average weight of all the 150 girls
=
=
= = 43.67 kg

Question 37 of 38
37. Question
The average of five multiple of 5 is (sbi 2001)
Correct
Average==15
Incorrect
=15

Question 38 of 38
38. Question
The average of eight numbers is x and the average of five of these is y. If the average of the remaining three is z, then :
Correct
Total of eight numbers = 8x
Total of five numbers = 5y
total of remaining three numbers = 8x – 5y.
But the given, total of remaining 3 numbers = 3z
so. 8x – 5y = 3z or 8x = 5y + 3Z.
Clearly, we have:X =
So, 8x = 5y + 3z.
Incorrect
Total of eight numbers = 8x
Total of five numbers = 5y
total of remaining three numbers = 8x – 5y.
But the given, total of remaining 3 numbers = 3z
so. 8x – 5y = 3z or 8x = 5y + 3Z.
Clearly, we have:X =
So, 8x = 5y + 3z.