The notion of averages involves summarizing a set of numbers by identifying a representative value situated, in some manner, at the midpoint of the data. Averages serve as valuable tools for comprehending and scrutinizing data, and they manifest in various types, each serving a distinct purpose.
Example 1: The run rate in cricket given for the first 10 overs was 3.2. Calculate the run rate in rest of the 40 overs in order to score 282 runs.
(a) 3.5
(b) 4.0
(c) 6.25
(d) Cannot be determined
Ans: (c)
= 250/40
= 6.25
Example 2: A shopkeeper has a sale of Rs. 6359, Rs. 2365, Rs. 5698, Rs. 5690, and Rs. 4560 for 5 successive months. Calculate his sale in the sixth month to make an average sale of Rs. 6400.
(a) 12348
(b) 13728
(c) 23614
(d) Cannot be determined
Ans: (b)
Sale for 5 months= 6359 + 2365 + 5698 + 5690 + 4560 = 24672
Required sale = (6400 x 6)  24672
= 38400 24672
= 13728
Example 3: When a new man joins a group of 8 people, their average age increases by 2.5kg. If he replaces a man weighing is 55 kg, how much does he weigh?
(a) 80
(b) 75
(c) 65
(d) Cannot be determined
Ans: (b)
Increased weight = (8 x 2.5) =20
Weight of the new man = (55 +20) = 75
Example 4: The average monthly income of A and B is Rs. 5050, that of B and C is Rs. 6250, and that of A and C is Rs. 5200. Calculate the monthly income of A.
(a) 3000
(b) 5000
(c) 4000
(d) Cannot be determined
Ans: (c)
A + B = 5050 x2 = 10100 (i)
B + C = 6250 x 2 = 12500(ii)
C + A = 5200 x 2 = 10400(iii)
Adding the above three equations, we get,
2 (A + B + C) = 33000
Or, A + B + C = 16500(iv)
When we subtract (ii) from (iv), we get
A = 4000
Therefore, A’s monthly income = Rs. 4000
Example 5: Ravi buys a petrol at Rs. 7.50, Rs. 8, and Rs. 8.50 for 3 months. Calculate the approximately average cost per liter of petrol if he spends Rs. 4000 each month.
(a) 8.0
(b) 7.98
(c) 10
(d) Cannot be determined
Ans: (b)
Total fuel consumed in 3 months
Total money spent = 3 x 4000 = 12000.
Therefore, average cost
= 6120/767
= 7.98
Example 6: In a family, two grandparents, three grandchildren, and two parents. 67 years is the average age of the grandparents. 35 years is the average age of the parents. 6 years is the average age of the children. Calculate the average age of the family.
(a) 25
(b) 40
(c) 31.71
(d) Cannot be determined
Ans: (c)
Family average age =
22/7
= 31.71
Example 7: If zero is the average of 20 numbers, then how many of them, at most must be greater than zero?
(a) 19
(b) 5
(c) 10
(d) Cannot be determined
Ans: (a)
Average = 0
Therefore, the sum of 20 numbers = 0 x 20 = 0
19 numbers among them may be positive.
If the sum of these numbers is a, then the 20th number is –a.
Example 8: 11 players make a football team. The captain’s age is 25 years. Age of the goalkeeper is 4 years more than that of the captain. The average age of the remaining team members except from these two is one year more than the entire team’s average age. What is the average age of the team?
(a) 31.5
(b) 32
(c) 26
(d) Cannot be determined
Ans: (a)
Average age of team = x
Therefore, 11x – (25 +29) = 9 (x+1)
11x – (25 +29) = 9 (x+1)
11x – 54 = 9x + 9
11x – 9x = 9 + 54
2x= 63
x = 63/2
= 31.5
Example 9: The average age of Alice, Bob, and Mike three years ago was 35 years. 5 years back the average age of Bob and Mike is 20 years. Determine Alice’s present age.
(a) 64
(b) 20
(c) 35
(d) Cannot be determined
Ans: (a)
Sum of present ages = (35 x 3 + 3 x 3) years = 114
present age of Bob and Mike = (20 x 2 + 5 x 2) years = 50
Therefore, Alice’s age = 114 – 50
= 64
Example 10: Ajay thinks that his weight is somewhere in between 65 and 72 kg. Ajay’s sister disagrees and says that his weight is more than 60 kg but less than 70 kg. His father thinks that his weight must not be more than 68 kg. If all of them are correct, what is the average possible weight of Ajay?
(a) 59
(b) 80
(c) 67
(d) Cannot be determined
Ans: (c)
Let Ajay’s weight = x kg
Age assumed by Ajay, 65 < X < 72
Age assumed by sister, 60 < X < 70.
Age assumed by father, X <= 68
Favourable values = 66, 67 and 68.
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