Average

 

What is Average?

The result obtained by adding several quantities together and then dividing this total by the number of quantities is called Average.

The main term of average is equal distribution of a value among all which may distribute persons or things. We obtain the average of a number using formula that is sum of observations divided by Number of observations.

Here is average based some fact and formula and some average shortcut tricks examples. The problem is given in Quantitative Aptitude which is a very essential paper in ssc exam. Given below are some more example for practicing.

Formula:

  • Average: = (Sum of observations / Number of observations).

 

Find the Average Speed

  • If a person travels a distance at a speed of x km/hr and the same distance at a speed of y km/hr then the average speed during the whole journey is given by-
  • If a person covers A km at x km/hr and B km at y km/hr and C km at z km/hr, then the average speed in covering the whole distance is-

When a person leaves the group and another person joins the group in place of that person then-

  • If the average age is increased,
    Age of new person = Age of separated person + (Increase in average × total number of persons)
  • If the average age is decreased,
    Age of new person
     = Age of separated person – (Decrease in average × total number of persons)

 

        When a person joins the group-In case of increase in average

  • Age of new member = Previous average + (Increase in average × Number of members including new member)

       

        In case of decrease in average

  • Age of new member = Previous average – (Decrease in average × Number of members including new member)

 

In the Arithmetic Progression there are two cases when the number of terms is odd and second one is when number of terms is even.

  • So when the number of terms is odd the average will be the middle term.
  • when the number of terms is even then the average will be the average of two middle terms.

 

Some Important Examples

 

Examples 1: what will be the average of 13, 14, 15, 16, 17?

Solution: Average is the middle term when the number of terms is odd, but before that let’s checks whether it is in A.P or not, since the common difference is same so the series is in A.P. So the middle term is 15 which is our average of the series.

 

Example 2: What will be the average of 13, 14, 15, 16, 17, 18?

Solution: We have discussed that when the number of terms are even then the average will be the average of two middle terms.

Now the two middle terms are 15 and 16, but before that the average we must check that the series should be A.P. Since the common difference is same for each of the term we can say that the series is in A.P. and the average is (16+15)/2 = 15.5

Example 3:The average of five numbers is 29. If one number is excluded the average becomes 27. What is the excluded number ?

Answer :

let the excluded number is

= (29 x 5) – ( 27 x 4 )

= 145 – 108

= 37 .

Example 4: Find the average of first 20 natural numbers?

Answer:

Sum of first n natural numbers = n ( n + 1 ) /2

So, we can find easily average of first 20 natural numbers 20 x 21 / 2 = 210

So, then Required average is = 210 / 20 = 10.5.

 

 

Example 5

Find the average of first 20 multiplies of 5 .

Answer:

Required average = 5 ( 1 + 2 + 3 +……………….. + 20) /20

= ( 5 x 20 x 21 / 20 x 2) = 2100 / 40 = 52.5 .

So the Required average is 52.5.

 

Questions:

Level-I:

1. In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
A. 6.25
B. 6.5
C. 6.75
D. 7

 

2. A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?
A.
28 4 years
7
B.
31 5 years
7
C.
32 1 years
7
D. None of these

 

3. A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
A. Rs. 4991
B. Rs. 5991
C. Rs. 6001
D. Rs. 6991

 

4. The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
A. 0
B. 1
C. 10
D. 19

 

5. The average weight of 8 person’s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
A. 76 kg
B. 76.5 kg
C. 85 kg
D. Data inadequate
E. None of these
 

 

6.

 

 

The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

A. 23 years
B. 24 years
C. 25 years
D. None of these

 

7. The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is:
A. 3500
B. 4000
C. 4050
D. 5000

 

8. The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:
A. 35 years
B. 40 years
C. 50 years
D. None of these

 

9. A car owner buys petrol at Rs.7.50, Rs. 8 and Rs. 8.50 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 4000 each year?
A. Rs. 7.98
B. Rs. 8
C. Rs. 8.50
D. Rs. 9

 

10. In Arun’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Arun’s weight is greater than 60 kg but less than 70 kg. His mother’s view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun?
A. 67 kg.
B. 68 kg.
C. 69 kg.
D. Data inadequate
E. None of these
 

 

 

 

 

11.

 

 

Level-II:

 

 

The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:

A. 17 kg
B. 20 kg
C. 26 kg
D. 31 kg

 

12. The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.
A. 47.55 kg
B. 48 kg
C. 48.55 kg
D. 49.25 kg

 

13. A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:
A. 250
B. 276
C. 280
D. 285

 

14. If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is:
A. 53.33
B. 54.68
C. 55
D. None of these

 

15. A pupil’s marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half (1/2). The number of pupils in the class is:
A. 10
B. 20
C. 40
D. 73
 

 

 

16.

 

 

The average age of P, Q, R and S is 30 years. How old is R?

I. The sum of ages of P and R is 60 years.
 II. S is 10 years younger than R.
A. I alone sufficient while II alone not sufficient to answer
B. II alone sufficient while I alone not sufficient to answer
C. Either I or II alone sufficient to answer
D. Both I and II are not sufficient to answer
E. Both I and II are necessary to answer

 

17.
How many candidates were interviewed everyday by the panel A out of the three panels A, B and C?
I. The three panels on average interview 15 candidates every day.
 II. Out of a total of 45 candidates interviewed everyday by the three panels, the number of candidates interviewed by panel A is more by 2 than the candidates interviewed by panel c and is more by 1 than the candidates interviewed by panel B.
A. I alone sufficient while II alone not sufficient to answer
B. II alone sufficient while I alone not sufficient to answer
C. Either I or II alone sufficient to answer
D. Both I and II are not sufficient to answer
E. Both I and II are necessary to answer

 

 

18.

 

What is the average age of children in the class?
I. The age of the teacher is as many years as the number of children.
 II. Average age is increased by 1 year if the teacher’s age is also included.
A. I alone sufficient while II alone not sufficient to answer
B. II alone sufficient while I alone not sufficient to answer
C. Either I or II alone sufficient to answer
D. Both I and II are not sufficient to answer
E. Both I and II are necessary to answer

 

 

Answers:

Level-I:

Answer:1 Option A

 

Explanation:

Required run rate = 282 – (3.2 x 10) = 250    = 6.25
40 40

 

 

Answer:2 Option B

 

Explanation:

Required average
= 67 x 2 + 35 x 2 + 6 x 3
2 + 2 + 3
= 134 + 70 + 18
7
= 222
7
= 31 5 years.
7

Answer:3 Option A

 

Explanation:

Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.

Required sale = Rs. [ (6500 x 6) – 34009 ]

= Rs. (39000 – 34009)

= Rs. 4991.

 

 

Answer:4 Option D

 

Explanation:

Average of 20 numbers = 0.

Sum of 20 numbers (0 x 20) = 0.

It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a).

 

 

Answer:5 Option C

 

Explanation:

Total weight increased = (8 x 2.5) kg = 20 kg.

Weight of new person = (65 + 20) kg = 85 kg.

 

Answer:6 Option A

 

Explanation:

Let the average age of the whole team by x years.

11x – (26 + 29) = 9(x -1)

11x – 9x = 46

2x = 46

x = 23.

So, average age of the team is 23 years.

 

Answer:7 Option B

 

Explanation:

Let P, Q and R represent their respective monthly incomes. Then, we have:

P + Q = (5050 x 2) = 10100 …. (i)

Q + R = (6250 x 2) = 12500 …. (ii)

P + R = (5200 x 2) = 10400 …. (iii)

Adding (i), (ii) and (iii), we get:  2(P + Q + R) = 33000  or   P + Q + R = 16500 …. (iv)

Subtracting (ii) from (iv), we get P = 4000.

  • P’s monthly income = Rs. 4000.

 

 

 

Answer:8 Option B

 

Explanation:

Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.

Sum of the present ages of wife and child = (20 x 2 + 5 x 2) years = 50 years.

Husband’s present age = (90 – 50) years = 40 years.

 

Answer:9 Option A

 

Explanation:

Total quantity of petrol
consumed in 3 years
= 4000 + 4000 + 4000  litres
7.50 8 8.50
= 4000 2 + 1 + 2  litres
15 8 17
= 76700  litres
51

Total amount spent = Rs. (3 x 4000) = Rs. 12000.

 Average cost = Rs. 12000 x 51 = Rs. 6120    = Rs. 7.98
76700 767

 

Answer:10 Option A

 

Explanation:

Let Arun’s weight by X kg.

According to Arun, 65 < X < 72

According to Arun’s brother, 60 < X < 70.

According to Arun’s mother, X <= 68

The values satisfying all the above conditions are 66, 67 and 68.

 Required average = 66 + 67 + 68 = 201 = 67 kg.
3 3

 

 

Level-II:

 

Answer:11 Option D

Explanation:

Let A, B, C represent their respective weights. Then, we have:

A + B + C = (45 x 3) = 135 …. (i)

A + B = (40 x 2) = 80 …. (ii)

B + C = (43 x 2) = 86 ….(iii)

Adding (ii) and (iii), we get: A + 2B + C = 166 …. (iv)

Subtracting (i) from (iv), we get : B = 31.

B’s weight = 31 kg.

 

Answer:12 Option C

 

Explanation:

Required average
= 50.25 x 16 + 45.15 x 8
16 + 8
= 804 + 361.20
24
= 1165.20
24
= 48.55

 

Answer:13 Option D

 

Explanation:

Since the month begins with a Sunday, to there will be five Sundays in the month.

Required average
= 510 x 5 + 240 x 25
30
= 8550
30
= 285

 

Answer:14 Option B

 

Explanation:

Required average
= 55 x 50 + 60 x 55 + 45 x 60
55 + 60 + 45
= 2750 + 3300 + 2700
160
= 8750
160
= 54.68

Answer:15 Option C

 

Explanation:

Let there be x pupils in the class.

Total increase in marks = x x 1 = x
2 2

 

x = (83 – 63) x = 20       x= 40.
2 2

Answer:16 Option D

 

Explanation:

P + Q + R + S = (30 x 4)       P + Q + R + S = 120 …. (i)

  1. P + R = 60 …. (ii)
  2. S = (R – 10) …. (iii)

From (i), (ii) and (iii), we cannot find R.

Correct answer is (D)

Answer:17 Option B

 

Explanation:

  1. Total candidates interviewed by 3 panels = (15 x 3) = 45.
  2. Let xcandidates be interviewed by C.

Number of candidates interviewed by A = (x + 2).

Number of candidates interviewed by B = (x + 1).

x + (x + 2) + (x + 1) = 45

3x = 42

x = 14

Hence, the correct answer is (B).

Answer:18 Option D

 

Explanation:

Let there be x children.

I gives, age of teacher = x years.

II gives, average age of (x + 1) persons = (x + 1) years.

Teacher’s age = (x + 1) (x + 1) – x2 = (x2 + 1 + 2x) – x2 = (1 + 2x)

Thus, teacher’s age cannot be obtained.

Correct answer is (D)