Practice Questions
Concept Explanation
Mixed average problems combine multiple concepts: basic average, addition/removal, replacement, weighted average, and average speed.
Strategy
- Identify the type: marks, age, speed, salary, or combined groups.
- Convert average to total sum first.
- Apply the correct formula for the change described.
- For speed, always use total distance / total time.
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Q1 Medium
Average of 5 numbers is 18. One number is removed and average becomes 16. The removed number is:
ExplanationOld sum = 90. New sum = 64. Removed = 26. -
Q2 Medium
Class A (20 students) average 55. Class B (30 students) average 65. Overall average is:
Explanation(1100 + 1950)/50 = 61. -
Q3 Hard
A car goes 80 km at 40 km/h and 80 km at 80 km/h. Average speed is:
ExplanationTotal 160 km in 2 + 1 = 3 hr. Average = 53.33 km/h (approx). -
Q4 Hard
Average age of 6 persons is 30. One aged 42 leaves and one aged 24 joins. New average is:
Explanation(180 − 42 + 24)/6 = 162/6 = 27 years. -
Q5 Medium
Average of 8 numbers is 25. Replace 30 with 50. New average is:
ExplanationSum increases by 20. New average = 25 + 20/8 = 27.5. -
Q6 Medium
10 kg at Rs. 40/kg mixed with 20 kg at Rs. 55/kg. Average price is:
Explanation(400 + 1100)/30 = Rs. 50 per kg. -
Q7 Medium
After 9 innings, average is 38. After 10th innings, average is 40. Tenth innings score is:
ExplanationOld sum = 342. New sum = 400. Tenth score = 58.
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Q8 Hard
Average of first 10 natural numbers and last 10 natural numbers (1 to 20) combined is:
ExplanationFirst 10 avg = 5.5, last 10 avg = 15.5. Combined = (55+155)/20 = 10.5. -
Q9 Medium
5 numbers have average 20. Adding 50 gives new average:
ExplanationSum = 100 + 50 = 150. Count = 6. New average = 150/6 = 25. -
Q10 Medium
Dept 1: 15 employees, avg Rs. 20,000. Dept 2: 25 employees, avg Rs. 28,000. Combined average is:
Explanation(300000 + 700000)/40 = Rs. 25,000. -
Q11 Medium
Average of 7 consecutive integers is 13. If 10 and 16 are removed, average of remaining 5 is:
ExplanationSet: 10 to 16, sum = 91. Remove 10 and 16: sum = 65, avg = 65/5 = 13. -
Q12 Medium
A journey of 120 km: 60 km at 30 km/h, 60 km at 60 km/h. Average speed is:
Explanation2×30×60/90 = 40 km/h. -
Q13 Medium
Average marks of 12 students is 50. One student's marks change from 40 to 70. New average is:
ExplanationSum increases by 30. New average = 50 + 30/12 = 52.5. -
Q14 Hard
Three groups of 10, 20 and 30 members have averages 40, 50 and 60. Combined average is:
Explanation(400 + 1000 + 1800)/60 = 53.33 (approx).
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DS1 Easy
What is the overall average?
Statement IGroup 1: 20 members, average 55.
Statement IIGroup 2: 30 members, average 65.
ExplanationNeed both groups. Overall average = 61. -
DS2 Medium
What is the average speed?
Statement ITotal distance is 160 km.
Statement IITotal time is 3 hours.
ExplanationNeed distance and time. Average speed = 160/3 = 53.33 km/h (approx).
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DS3 Medium
What is the removed number?
Statement IAverage of 5 numbers is 18.
Statement IIAfter removal, average of 4 numbers is 16.
ExplanationTogether: removed number = 90 − 64 = 26. -
DS4 Hard
Is the combined average above 60?
Statement IClass A: 20 students, average 55.
Statement IIClass B: 30 students, average 65.
ExplanationTogether: combined average = 61 > 60.