Average Practice Questions

5 questions per page • Detailed step-by-step solutions

Question 6
Hard
The average salary of all the workers in a workshop is ₹17080. The average salary of 11 technicians is ₹28000 and the average salary of the rest is ₹14000. What is the total number of workers in the workshop?
A 50
B 39
C 61
D 52
Correct Answer: A

Explanation:

Step 1: Let the total number of workers be n. Total salary: 11 × 28000 + (n − 11) × 14000 = n × 17080. Step 2: 308000 + 14000n − 154000 = 17080n → (17080 − 14000)n = 308000 − 154000 → 3080n = 154000. Step 3: n = 154000 ÷ 3080 = 50.
Question 7
Medium
What is the average of the cubes of the first 16 natural numbers?
A 1156
B 614.12
C 1140
D 1088
Correct Answer: A

Explanation:

Step 1: Sum of cubes 1³ + 2³ + … + n³ = [n(n + 1)/2]² = [136]² = 18496. Step 2: Number of terms = 16. Step 3: Average = 18496 ÷ 16 = 1156.
Question 8
Medium
What is the average of the squares of the first 11 natural numbers?
A 46
B 36
C 92
D 57
Correct Answer: A

Explanation:

Step 1: Sum of squares 1² + 2² + … + n² = n(n + 1)(2n + 1)/6 = 11 × 12 × 23/6 = 506. Step 2: Number of terms = 11. Step 3: Average = 506 ÷ 11 = 46.
Question 9
Medium
A man's average monthly expenditure for the first 3 months of a year was ₹17000, and for the remaining 9 months it was ₹17500. If he saved ₹24000 during the year, what was his average monthly income?
A ₹19250
B ₹19875
C ₹18875
D ₹19375
Correct Answer: D

Explanation:

Step 1: Total expenditure for the year = 3 × 17000 + 9 × 17500 = 51000 + 157500 = 208500. Step 2: Annual income = expenditure + saving = 208500 + 24000 = 232500. Step 3: Average monthly income = 232500 ÷ 12 = ₹19375.
Question 10
Easy
What is the average of the first 144 natural numbers?
A 72
B 73
C 72.5
D 145
Correct Answer: C

Explanation:

Step 1: Sum of the first n natural numbers = n(n + 1)/2 = 144 × 145/2 = 10440. Step 2: Number of terms = 144. Step 3: Average = 10440 ÷ 144 = 72.5.