1. Find the average of first 67 numbers.
Sol:
average = \(\frac{{\frac{{n(n + 1)}}{2}}}{n}\) = \(\frac{{n + 1}}{2}\) = \(\frac{{67 + 1}}{2}\) = 34 Answer
2. The average of 35 numbers is 380. If each of the number is divided by 19. Find the new average.
Sol:
New Average = \(\frac{{old\;average}}{{19}}\) = \(\frac{{380}}{{19}}\) = 20 Answer
3. The average of 9 result is 60. If the average of first 5 result is 50 and the average of last 5 result is 70 then find the 5ᵗʰ result.
Sol:
Method(1):
5ᵗʰ result = 5 × 50 + 5 × 70 – 9 × 60 = 60 Answer
4. The average of 50 numbers is 45. The average of 50 numbers and 3 new number is 51. Then find the average of three new numbers.
Sol:
Method(1):
Sum of three numbers = (50 + 3)×51 – 50×45
= 453
∴ average of three new numbers = \(\frac{{453}}{3}\) = 151 Answer
Method(2):
Increase in average = 51 – 45 = 6
A = 45
N = 50
n = 3
∴ Average of new numbers = A + \(\left( {1 + \frac{N}{n}} \right)\).x
= 45 + \(\left( {1 + \frac{{50}}{3}} \right)\).6
= 151 Answer
Method(3):
5. The average salary of 30 workers in an office is Rs. 2400 per month. If the manager’s salary is added, the average becomes Rs. 2500 per month. Find the manager’s annual salary.
Sol:
Method(1):
Manager’s per month salary = (30 + 1)×2500 – 30×2400
= 5500
∴ annual salary of manager = 5500×12
= 66000 Rs. Answer
Method(2):
N = 30
x = 2500 – 2400 = 100
A = 2400
n = 1
∴ per month salary of manager = A + \(\left( {1 + \frac{N}{n}} \right).x\)
= 2400 + \(\left( {1 + \frac{{30}}{1}} \right).100\)
= 5500
∴ annual salary of manager = 5500 × 12
= 66000 Rs. Answer
Method(3):
6. In a class there are 10 students at the age of 15 years. 15 students at the age of 10 years and 22 students of age 18 years. What is the average age of a student ?
Sol:
Method(1):
Average age of a student = \(\frac{{10 \times 15 + 15 \times 10 + 22 \times 18}}{{10 + 15 + 22}}\)
= \(\frac{{696}}{{47}}\)
= \(14\frac{{38}}{{47}}\) years/student Answer
Method(2):
7. A zoo has an average of 600 visitors on sunday and 390 visitors on other days. the average number of visitors per day in a month at 30 day beginning with sunday will be How many ?
Sol:
If the month starts with sunday then there will be 5 sunday in the month
8. The average age of 44 students in a class is 21 years. If the teacher’s age is included then average becomes 21 year 6 months. Find the age of teacher.
Sol:
Method(1):
Age of teacher = (44 + 1)21.5 – 44×21
= 43.5 year Answer
Method(2):
A = 21
N = 44
n = 1
x = 0.5
age of teacher = A + \(\left( {1 + \frac{N}{1}} \right).x\)
= 21 + \(\left( {1 + \frac{{44}}{1}} \right)0.5\)
= 43.5 years Answer
Method(3):
9. Find the average of following 12 numbers:
2, 10, 7, 9, 13, 12, 14, 18, 19, 5, 8, 3
Sol:
Method(1):
Average = \(\frac{{2 + 10 + 7 + 9 + 13 + 126 + 14 + 18 + 19 + 5 + 8 + 3}}{{12}}\)
= 10 Answer
Method(2):
10. Group A has 10 elements and their average is 5, Group B has 20 elements and their average is 8. If elements of these two groups are combined to form a third group C. Then find the average of Group C ?
Sol:
Method(1):
Average = \(\frac{{10 \times 5 + 20 \times 8}}{{10 + 20}}\) = 7 Answer
Method(2):
Using Alligation: