Averages Aptitude Questions with Solutions
36 Averages questions with hints, worked solutions and time targets — 20 easy · 14 medium · 2 hard.
- Section: Quantitative Aptitude
- Questions: 36
- By difficulty: 20 easy · 14 medium · 2 hard
- Cost: Free, unlimited on every plan
Weighted means, the effect of adding or removing a member, and deviation tricks.
Averages: the essentials
- Average = sum ÷ count, so sum = average × count. Work in totals and divide once, at the end.
- An evenly spaced list averages (first + last)/2, the middle of the list. The average of 1 to n is (n + 1)/2; of the first n even numbers, n + 1; of the first n odd numbers, n.
- Newcomer: if one person raises the average of n people by d, the newcomer = new average + n × d.
- Replacement: new member = departing member + n × (change in average).
- Misread entry: the average moves by (correct − wrong) ÷ n.
- Removal: the removed value = old total − new total.
- Combined average = (n₁a₁ + n₂a₂) ÷ (n₁ + n₂). It leans towards the larger group and is never simply the mean of the two averages.
- Overlapping groups, such as the first six and last six of eleven results: the shared value = sum of the group totals − overall total.
- Multiplying every value by k multiplies the average by k; adding k to every value adds k.
- Average speed over equal distances is 2ab/(a + b), not (a + b)/2.
Example: a batsman averaging 32 over 11 innings scores 68 in the 12th. The average rises by (68 − 32)/12 = 3, to 35.
Questions
- The teacher joins the class Easy
The average age of 30 students is 15 years. When the teacher's age is included, the average becomes 16. How old is the teacher? - One person replaced Easy
The average weight of 8 people increases by 2.5 kg when a person weighing 65 kg is replaced by a new one. What is the new person's weight? - Five consecutive even numbers Easy
The average of five consecutive even numbers is 24. What is the largest of them? - A number was misread Easy
The average of 10 numbers was calculated as 42. It was then found that one number, 64, had been read as 46. What is the correct average? - A big score in the 17th innings Easy
A batsman's average after 16 innings is 40. He scores 91 in the 17th innings. What is his new average? - Average of the first 50 natural numbers Easy
What is the average of the first 50 natural numbers? - Average of the primes between 30 and 50 Medium
What is the average of all prime numbers between 30 and 50? - Average of the first five multiples of 3 Easy
What is the average of the first five multiples of 3? - Average of the even numbers to 50 Easy
What is the average of all even numbers from 2 to 50? - Average of the squares of the first five naturals Easy
What is the average of the squares of the first five natural numbers? - The teacher joins the class Easy
The average age of 30 students is 15 years. When the teacher's age is included the average becomes 16. How old is the teacher? - A manager joins the company Medium
The average salary of 20 employees is ₹15,000. When the manager's salary is added the average rises by ₹500. What is the manager's salary? - One person is replaced Easy
The average weight of 8 people increases by 2.5 kg when a person weighing 65 kg is replaced by someone new. What is the new person's weight? - A number was misread Easy
The average of 10 numbers was found to be 42. It was later noticed that 64 had been read as 46. What is the correct average? - Combining two groups Easy
The average of 30 results is 20 and the average of 20 other results is 30. What is the average of all 50? - Two classes together Medium
A class of 30 students averages 40 marks and another of 50 students averages 60 marks. What is the combined average? - Three sections of a year group Medium
Three classes have 25, 30 and 45 students with average marks 50, 60 and 70 respectively. What is the overall average? - A score in the 17th innings Easy
A batsman's average after 16 innings is 40. He scores 91 in the 17th. What is his new average? - Runs needed to raise the average Medium
A cricketer has an average of 48 runs in 12 innings. How many runs must he score in the 13th innings to raise his average by 5? - The fourth innings Easy
A player's average after 3 innings is 42. After the 4th his average becomes 44. How many runs did he score in the 4th? - One number is excluded Easy
The average of 5 numbers is 27. When one number is excluded the average becomes 25. What was the excluded number? - A new observation is added Easy
The average of 6 observations is 12. A new observation is included and the average becomes 13. What is the new observation? - Two numbers discarded Medium
The average of 50 numbers is 38. If the numbers 45 and 55 are discarded, what is the average of the rest? - Finding the sixth result Medium
The average of 11 results is 50. The average of the first six is 49 and of the last six is 52. What is the sixth result? - The middle number of eleven Medium
The average of 11 numbers is 10.9. If the average of the first six is 10.5 and of the last six is 11.4, what is the sixth number? - The weight of B Medium
The average weight of A, B and C is 45 kg. The average of A and B is 40 kg and of B and C is 43 kg. What is B's weight? - Technicians and the rest Hard
The average salary of all workers in a workshop is ₹8,000. The average of 7 technicians is ₹12,000 and of the remaining workers ₹6,000. - Three pairs of numbers Medium
The average of 6 numbers is 3.95. The average of two of them is 3.4 and of another two is 3.85. What is the average of the remaining two? - Temperatures across four days Hard
The average temperature for Monday, Tuesday and Wednesday was 37°, and for Tuesday, Wednesday and Thursday it was 34°. - Average monthly income Medium
A man's average monthly expenditure for the first 3 months was ₹2,200 and for the next 9 months ₹1,800. He saved ₹1,200 during the year. - A family five years on Medium
The average age of a husband and wife was 23 years when they married. Five years later they have a one-year-old child. - Seven consecutive numbers Easy
The average of seven consecutive numbers is 20. What is the largest of them? - Five consecutive even numbers, the smallest Easy
The average of five consecutive even numbers is 24. What is the smallest of them? - Scaling every number Easy
The average of 8 numbers is 20. If each number is multiplied by 3, what is the new average? - How many can be positive Medium
The average of 20 numbers is zero. At most how many of them may be greater than zero? - Average speed over two legs Medium
A car covers 100 km at 60 km/h and another 100 km at 40 km/h. What is its average speed for the whole journey?
Placement tests that ask averages
- Thirty-Minute Sprint CodeKairo
- Full-Length Aptitude Paper CodeKairo
- TCS NQT — Foundation TCS
- TCS NQT — Foundation + Advanced TCS
- Infosys SE / DSE — Aptitude Infosys
- Wipro NLTH — Aptitude Wipro
- Accenture — Cognitive & Technical Accenture
- Cognizant GenC — Aptitude Cognizant
- HCLTech — Written Test HCLTech
- Tech Mahindra — Aptitude & Technical Tech Mahindra
- LTIMindtree — Online Assessment LTIMindtree
- Mphasis — AMCAT Assessment Mphasis
- Virtusa — Online Test & Coder Challenge Virtusa
- Goldman Sachs — Aptitude Test Goldman Sachs
- Deloitte — Online Assessment Deloitte
- Adobe — Campus Aptitude Adobe
- ZS Associates — Aptitude ZS Associates
- Morgan Stanley — Aptitude & Technical Morgan Stanley
- Oracle — Aptitude & Verbal Oracle
- Zoho — Round 1 Zoho