Practice Questions
Concept Explanation
When a new value is added to a set, the new average is:
New average = (Old sum + New value) / (n + 1)
Key Idea
- Old sum = Old average × n
- New sum = Old sum + added value
- Change in average = (New value − Old average) / (n + 1)
Placement Shortcut
Find the old total first. Add the new value, then divide by the new count.
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Q1 EasyThe average age of 30 students of a class is 9 years. If the age of their teacher is included, the average age increases by 1 year. The age of the teacher is:ExplanationOld sum of ages of 30 students = 30 × 9 = 270 years. When the teacher is included, count = 31 and average = 9 + 1 = 10, so new sum = 31 × 10 = 310 years. Age of the teacher = 310 − 270 = 40 years. Hence the answer is 40 years.
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Q2 EasyThe average of 8 numbers is 27. If one more number is included, the average becomes 28. The included number is:ExplanationOld sum = 8 × 27 = 216. New sum of 9 numbers = 9 × 28 = 252. Included number = 252 − 216 = 36. Hence the answer is 36.
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Q3 EasyThe average of 5 numbers is 20. If a sixth number 50 is added, the new average is:ExplanationOld sum = 5 × 20 = 100. New sum = 100 + 50 = 150. New average = 150 / 6 = 25. Hence the answer is 25.
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Q4 EasyThe average marks of 9 students is 45. A new student scoring 75 joins the group. The new average is:ExplanationOld sum = 9 × 45 = 405. New sum = 405 + 75 = 480. New average = 480 / 10 = 48. Hence the answer is 48.
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Q5 EasyThe average of 15 numbers is 28. If a number equal to the old average is added, the new average is:ExplanationOld sum = 15 × 28 = 420. Adding 28 gives new sum = 448 and new count = 16. New average = 448 / 16 = 28. Adding a value equal to the current average leaves the average unchanged. Hence the answer is 28.
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Q6 MediumThe average weight of 8 persons increases by 2.5 kg when one person of 60 kg is replaced by a new person. What is the weight of the new person?ExplanationIncrease in total weight = 8 × 2.5 = 20 kg. When a 60 kg person is replaced, the new person must weigh 60 + 20 = 80 kg so that the total increases by 20 kg and the average rises by 2.5 kg. Hence the weight of the new person is 80 kg.
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Q7 MediumThe average salary of 20 workers in an office is Rs. 1900 per month. If the manager's salary is added, the average becomes Rs. 2000 per month. The manager's monthly salary is:ExplanationSum of salaries of 20 workers = 20 × 1900 = 38000. After including the manager, sum of 21 salaries = 21 × 2000 = 42000. Manager's salary = 42000 − 38000 = 4000. Hence the answer is Rs. 4000.
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Q8 MediumThe average age of 24 boys and their teacher is 15 years. When the teacher's age is excluded, the average decreases by 1 year. The age of the teacher is:ExplanationIncluding the teacher there are 25 persons with average 15, so total age = 25 × 15 = 375 years. Excluding the teacher, 24 boys have average 14, so their total = 24 × 14 = 336 years. Teacher's age = 375 − 336 = 39 years. Hence the answer is 39 years.
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Q9 MediumThe average of 12 numbers is 18. One more number is added and the average becomes 20. The added number is:ExplanationOld sum = 12 × 18 = 216. New sum of 13 numbers = 13 × 20 = 260. Added number = 260 − 216 = 44. Hence the answer is 44.
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Q10 MediumThe average weight of 5 men is 65 kg. A man weighing 80 kg joins them. The new average weight is:ExplanationOld sum = 5 × 65 = 325 kg. New sum = 325 + 80 = 405 kg. New average = 405 / 6 = 67.5 kg. Hence the answer is 67.5 kg.
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Q11 MediumThe average of 6 numbers is 18. One more number is added and the average becomes 20. The added number is:ExplanationOld sum = 6 × 18 = 108. New sum of 7 numbers = 7 × 20 = 140. Added number = 140 − 108 = 32. Hence the answer is 32.
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Q12 MediumThe average age of a class of 22 students is 21 years. The average increases by 1 year when the teacher's age also is included. The age of the teacher is:ExplanationOld sum = 22 × 21 = 462 years. New average of 23 persons = 22 years, so new sum = 23 × 22 = 506 years. Teacher's age = 506 − 462 = 44 years. Hence the answer is 44 years.
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Q13 HardA batsman has a certain average of runs for 10 innings. In the eleventh inning he scores 100 runs, thereby increasing his average by 5 runs. His new average is:ExplanationLet the old average be A. Then (10A + 100) / 11 = A + 5. Multiply both sides by 11: 10A + 100 = 11A + 55 ⇒ 100 − 55 = 11A − 10A ⇒ A = 45. New average = A + 5 = 50. Hence the answer is 50.
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Q14 HardA batsman's average after 10 innings is 40. To raise his average to 44 after the 11th innings, he must score:ExplanationRequired total after 11 innings = 11 × 44 = 484. Current total after 10 innings = 10 × 40 = 400. Runs needed in the 11th innings = 484 − 400 = 84. Hence the answer is 84.
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DS1 Easy
Trainees add one score to a data set. What is the new average after adding one number?
Statement IThe average of 6 numbers is 20.
Statement IIThe number added is 32.
ExplanationNew average = (Old sum + added value) / (n + 1). Statement I: Old sum = 120, but the added value is unknown. Statement II: Added value = 32, but old sum is unknown. Together: New average = (120 + 32) / 7 = 152 / 7 = 21 5/7. Both are needed. Answer: C. -
DS2 Easy
Is the new average greater than the old average?
Statement IThe added number is 50.
Statement IIThe old average is 45.
ExplanationA newly added value raises the average if and only if it exceeds the old average. Statement I alone does not give the old average. Statement II alone does not give the added value. Together: 50 > 45, so the new average is greater. Both are needed. Answer: C.
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DS3 Medium
For the value that was appended to a list. What is the added number?
Statement IThe average of 8 numbers is 25.
Statement IIAfter addition, the average of 9 numbers is 27.
ExplanationAdded number = New sum − Old sum. Statement I: Old sum = 200. Statement II: New sum = 243. Alone, neither gives both sums. Together: Added number = 243 − 200 = 43. Both are needed. Answer: C. -
DS4 Medium
A company drill asks for the average after one more observation is included. What is the new average?
Statement IThere are 5 numbers with average 18.
Statement IIA sixth number equal to 18 is added.
ExplanationStatement I: Old sum = 90, but without knowing what is added the new average is unknown. Statement II: Says 18 is added, but without old sum/count the result is unknown. Together: New sum = 90 + 18 = 108; new average = 108 / 6 = 18. Both are needed. Answer: C.