Averages: Concepts and Questions for Competitive Exams

Answers to Averages Practice Questions:

1. The average of 5 numbers is 12. If one of the numbers is 15, what is the average of the other 4 numbers?

• Answer:
  The sum of 5 numbers = $12 \times 5 = 60$12×5=60.
  Subtracting the number 15: $$60 – 15 = 45$$60−15=45 The average of the remaining 4 numbers = $\frac{45}{4} = 11.25$445​=11.25.

2. The average of 10 numbers is 25. If one of the numbers is 10, what is the average of the remaining 9 numbers?

• Answer:
  The sum of 10 numbers = $25 \times 10 = 250$25×10=250.
  Subtracting the number 10: $$250 – 10 = 240$$250−10=240 The average of the remaining 9 numbers = $\frac{240}{9} = 26.67$9240​=26.67.

3. The average of 8 numbers is 20. If one number is excluded, the average becomes 22. What is the excluded number?

• Answer:
  The sum of 8 numbers = $20 \times 8 = 160$20×8=160.
  The sum of the remaining 7 numbers = $22 \times 7 = 154$22×7=154.
  The excluded number = $160 – 154 = 6$160−154=6.

4. The average of 5 consecutive odd numbers is 35. Find the smallest of these numbers.

• Answer:
  The sum of 5 consecutive odd numbers = $35 \times 5 = 175$35×5=175.
  The middle number (since it’s an odd sequence) = $\frac{175}{5} = 35$5175​=35.
  The numbers are $33, 35, 37, 39, 41$33,35,37,39,41.
  The smallest number = 33.

5. The average age of a group of 6 persons is 25 years. If one person leaves the group and the average age becomes 24 years, what is the age of the person who left?

• Answer:
  The total age of 6 persons = $25 \times 6 = 150$25×6=150.
  The total age of 5 persons = $24 \times 5 = 120$24×5=120.
  The age of the person who left = $150 – 120 = 30$150−120=30.

6. The average weight of 3 persons is 60 kg. If one of the persons weighs 75 kg, find the average weight of the other two persons.

• Answer:
  The total weight of 3 persons = $60 \times 3 = 180$60×3=180.
  The weight of the other 2 persons = $180 – 75 = 105$180−75=105.
  The average weight of the remaining two persons = $\frac{105}{2} = 52.5 \, \text{kg}$2105​=52.5kg.

7. The average of 50 numbers is 100. The sum of the first 25 numbers is 2400. What is the sum of the last 25 numbers?

• Answer:
  The total sum of 50 numbers = $100 \times 50 = 5000$100×50=5000.
  The sum of the last 25 numbers = $5000 – 2400 = 2600$5000−2400=2600.

8. The average of three numbers is 28. If two of the numbers are 25 and 30, find the third number.

• Answer:
  The sum of the three numbers = $28 \times 3 = 84$28×3=84.
  The sum of the two known numbers = $25 + 30 = 55$25+30=55.
  The third number = $84 – 55 = 29$84−55=29.

9. The average of 5 numbers is 80. If one number is 90, find the average of the remaining 4 numbers.

• Answer:
  The sum of the 5 numbers = $80 \times 5 = 400$80×5=400.
  The sum of the remaining 4 numbers = $400 – 90 = 310$400−90=310.
  The average of the remaining 4 numbers = $\frac{310}{4} = 77.5$4310​=77.5.

10. The average score of 40 students in a class is 60. If the score of one student is 100, what is the average score of the remaining students?

Answer:
The total score of 40 students = $60 \times 40 = 2400$60×40=2400.
The total score of the remaining 39 students = $2400 – 100 = 2300$2400−100=2300.
The average score of the remaining students = $\frac{2300}{39} \approx 59$392300​≈59.