Friday, 8 January 2016

Aptitude Questions - Averages

Problems on Averages
1.    Average = Sum of the observations/Number of Observations. In short form Average is also known as Mean or Arithmetic Mean
2.    Sum of observations = Average x Number of Observations
3.    Number of Observations = Sum of observations / Average
4.    Average of N consecutive natural or even or odd numbers or multiples of any number (i.e, numbers which are in Arithmetic Progression A.P) is the middle number. If N is the odd number.
Example: Average of 23, 25,27,29,31. Here we have 5 consecutive odd numbers. So the average is middle number 27
If N is the even number, it is the average of the middle two numbers
Example: Average of 36, 42, 48,54,60,66. These are 6 consecutive multiples of 6. So the average of these numbers is average of middle 2 numbers.
5.     Whatever change occurs to each number, the same change is applicable to the average also.
Example: The average of 13 observations is 28. If 5 is added to each number, then the average is similarly changed. The new average will be 28+5= 33
6.    If average of m observations is x and n observations is y, then average of (m+n) observations is (mx + ny)/m+n

Aptitude Questions on Averages:
Arithmetic Questions with Answers – Averages
1.    Find the average of 83,92,112,137,100?
Explanation :  Average = Sum of the observations/Number of Observations
             Average = (83+92+112+137+100)/5
                          = 524/5 =104.8

Bank Clerks Test Free Study Material – Questions with Answers
2.    Average of 15 quantities is 25 and average of 10 quantities is 35. Find the average of all the 25 quantities?
Explanation : If average of m observations is x and n observations is y, then average of (m+n) observations is (mx + ny)/m+n
            Here m=15  x= 25   and n=10 , y=35
                   Avearge of all the 25 quantities = (15 x 25  + 10 x 35)/ 15+10
                                                              = (375+350)/25 = 725/25= 29


Averages Solved Examples with Solutions
3.    The average expenditure of a worker for first 5 months is Rs 3500 and average expenditure for last 7 months is Rs 4500 and his savings are Rs 11000. Find his average monthly income?
Explanation:
Income = Expenditure + Savings
Total expenditure for year = 5 x 3500 + 7 x 4500 = 49000
Savings = Rs 11000
Total annual income= Annual Expenditure + Annual savings = 49000+11000 = 60000
Average monthly income = 60000/12= Rs 5000

GMAT Mathematics Free study material – Averages and Applications
4.    An average mark of a student in 8 subjects is 56. His marks in 7 subjects are 60,48,56,58,52, 71 AND 67. Find the marks in the 8th subject?
Explanation : Sum of the marks in 8 subjects = 8 x 56 =448
 Sum of the marks in 7 subjects = 60+48+56+58+52+71+67 = 412
          Marks in the 8th subject = Marks in 8 subjects - marks in 7 subjects
                                                     = 448 -412 =36
Arithmetic Questions with Answers – Problems on  Averages
5.    The total marks obtained by a student in Arithmetic, Reasoning, English, Mathematics, Computer science were 315. He got 60 marks in Arithmetic. His average marks in English, Mathematics and Computer science were 61.5. Find his marks in Reasoning
Explanation: Total marks in A +R +E+M+CS = 315
   Marks in Arithmetic A= 60
Average marks in E, M and CS = 61.5 => (E+M+CS) /3 = 61.5 =>E+M+CS=184.5
   Marks in English E => (A +R +E+M+CS)- (A + E+M+CS)
                             = 315 – (60+184.5)=315-244.5 = 70.5

Aptitude Questions and Answers for Competitive Examinations - Averages
6.    The average score of a player in 9 matches is 36.iF in the 10th match his score is 48.What is his new average score?
Explanation : Total score for all 10 matches = total score in 9 matches + score in 10th match = ( 9 x36) +48 = 384
   Average score in 10 matches = 384/10 = 38.4

Aptitude Questions for Campus Placements – Averages
7.    The average of 11 numbers is 45. The average of first 5 numbers is 48 and the average of last 5 numbers is 36. Find the sixth number?
Explanation :
     Sum of 11 numbers = 11 x 45 =495
 Sum of first 5 numbers = 5 x48= 240
Sum of last 5 numbers =  5 x 36 = 180
 6th number = Sum of 11 numbers – (Sum of first 5 numbers + sum of the last 5 numbers)8
= 495 –(240+180)= 495-420=75

SBI Bank Clerks free study material - Averages
8.    The average of 13 observations is 25. The average of first 7 observations is 28 and that of last 7 observations is 26.What is the value of 7th observation?
Explanation: Sum of 13 observations = 13 x 25 = 325
   Sum of 1st 7 observations + Sum of last 7 observations
= 7 x 28 + 7 x 26=196+182=378
( It is sum of 14 observations, here 7th observation repeated while adding observations)
Therefore 7th observation = Sum of 14 observations – Sum of 13 observations
                                   = 378- 325 =53

Aptitude Questions and Answers for Competitive Examinations - Averages
9.    The average runs of 11 players of a cricket team were 32. If the runs of the captain were excluded, then average would become 33.Find the score of the captain?
Explanation: Sum of the scores of 11 players = 11 x 32 =352
  When runs of the captain excluded, sum of the scores of 10 players = 10 x33 = 330
Score of the captain = Score of 11 players – Score of 10 players
                             = 352-330 = 22

Arithmetic Questions with Answers – Problems on  Averages
10. The average of 15 numbers is 36. The average of first 5 numbers is 38 and average of last 5 numbers is 40. Find the average of middle 5 numbers?
Explanation: Sum of middle 5 numbers = Sum of 15 numbers –(sum of first 5 numbers + sum of last 5 numbers)
Sum of middle 5 numbers = (15x36)-(5x38 + 5x40)
                                    =   540-(190+200) =540- 390=150
Average of middle 5 numbers=150/5 = 30.

IIM-CAT Quantitative Aptitude free study material – Problems on Average
11. The average age of 20 students is 14 years. If the age of the teacher is added, the average will be increased by 2 years. What is the age of the teacher?
Explanation :
   Including teacher, there are 21 members.
   Total age of 20 students + 1 teacher = 21 x 16 =336
   Total age of 20 students                 =  20x 14  =280
       Age of the teacher= 336 – 280 =56 years

IBPS PO Exams Aptitude Questions – Problems on Averages
12. The average age of 25 students in a class is 15 years. If the ages of two teachers are added, the average becomes 17. What is the sum of the ages of two teachers?
Explanation:
Sum of the ages of 25 students + 2 teachers = 27 x 17 = 459.
Sum of the ages of 25 students                   = 25 x 15 =  375
 Therefore sum of the ages of 2 teachers = 459-375 = 84

GMAT Quantitative Aptitude – Problems on Averages
13. The average salary of 30 employees in organization is Rs 12500. If each employee gets a salary hike of Rs 1250, find their new average salary?
Explanation:  If each element in the group is increased by same number or decreased by same number, the average changes by same number.
As each employee’s salary is increased by Rs 1250, their new average salary= Rs 12500+ 1250 = Rs 13750

Bank Clerks Test Free Study Material – Questions with Answers
14. The average of 15 observations is 36. If each observation is divided by 4, find the average of new observations?
Explanation: If each observation is in the data set is multiplied or divided by same value, their average changes similarly.

Given that each  observation is divided by 4, hence their new average = Previous Average /4 = 36/4 =9