Practice Questions
Concept Explanation
When one value is replaced by another, the count stays the same but the sum changes.
New average = (Old sum − Old value + New value) / n
Key Idea
- Change in sum = New value − Old value
- Change in average = (New value − Old value) / n
Example
Average of 5 numbers is 20 (sum 100). Replace 15 with 25: new sum = 110, new average = 22.
-
Q1 EasyThe average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What is the weight of the new person?ExplanationFormula: New weight = Old weight + (n × increase in average). Total weight rises by 8 × 2.5 = 20 kg when 65 kg is replaced. Therefore new weight = 65 + 20 = 85 kg.
-
Q2 EasyAverage of four consecutive even numbers is 27. Largest is:ExplanationLet the four consecutive even numbers be x, x + 2, x + 4 and x + 6. Their average = (4x + 12) / 4 = x + 3 = 27 → x = 24. The numbers are 24, 26, 28 and 30. Largest = 30.
-
Q3 EasyThe average of 5 numbers is 20. If one number 15 is replaced by 25, the new average is:ExplanationOld sum = 5 × 20 = 100. New sum = 100 − 15 + 25 = 110. New average = 110 / 5 = 22.
-
Q4 EasyIn a class of 40, average marks are 60. If one score of 40 is replaced by 80, the new average is:ExplanationOld sum = 40 × 60 = 2400. New sum = 2400 − 40 + 80 = 2440. New average = 2440 / 40 = 61.
-
Q5 MediumWhen a student weighing 45 kgs left a class of 30 students, the average weight of the remaining 29 students increased by 300 g. What was the average weight of all the 30 students?ExplanationLet the average of 30 students be x kg. Then 30x − 45 = 29(x + 0.3). Expanding: 30x − 45 = 29x + 8.7 → x = 53.7. So the average weight of all 30 students was 53.7 kg.
-
Q6 MediumThe average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4?ExplanationPresent total = 10 × 32 = 320. Required average after 11 innings = 36, so required total = 11 × 36 = 396. Runs needed in the 11th innings = 396 − 320 = 76.
-
Q7 MediumThe average of 9 numbers is 40. If one number 55 is replaced by 37, what is the new average?ExplanationOld sum = 9 × 40 = 360. Change in sum = 37 − 55 = −18. New sum = 360 − 18 = 342. New average = 342 / 9 = 38.
-
Q8 MediumThe average weight of 10 students is 55 kg. If one student of 60 kg is replaced by another of 72 kg, the new average weight is:ExplanationOld sum = 10 × 55 = 550 kg. Net increase = 72 − 60 = 12 kg. New sum = 562 kg. New average = 562 / 10 = 56.2 kg.
-
Q9 MediumThe average of 8 numbers is 22. The highest number 40 is replaced by 32. The new average is:ExplanationOld sum = 8 × 22 = 176. New sum = 176 − 40 + 32 = 168. New average = 168 / 8 = 21.
-
Q10 MediumThe average of 7 numbers is 35. If 42 is replaced by 28, by how much does the average change?ExplanationChange in sum = 28 − 42 = −14. Change in average = −14 / 7 = −2. The average decreases by 2.
-
Q11 HardAverage of 20 numbers is zero. Of them, at most how many can be greater than zero?ExplanationIf the average is zero, the algebraic sum of all 20 numbers is zero. At most 19 numbers can be positive if the remaining one is a sufficiently large negative number that cancels their sum. All 20 cannot be positive. Hence at most 19.
-
Q12 HardAverage of 12 numbers is 15. Two numbers 10 and 8 are replaced by 22 and 20. The new average is:ExplanationOld sum = 12 × 15 = 180. Net change = (22 + 20) − (10 + 8) = 42 − 18 = 24. New sum = 180 + 24 = 204. New average = 204 / 12 = 17.
-
Q13 HardAverage of 15 numbers is 48. One number wrongly entered as 36 is corrected to 63. The correct average is:ExplanationCorrection increases the sum by 63 − 36 = 27. Increase in average = 27 / 15 = 1.8. Correct average = 48 + 1.8 = 49.8.
-
Q14 HardAverage of 6 numbers is 18. Replacing one number x by 30 raises the average to 20. Find x.ExplanationOld sum = 6 × 18 = 108. New sum = 6 × 20 = 120. So 30 − x = 120 − 108 = 12 → x = 30 − 12 = 18.
-
DS1 Easy
In a campus quant drill on replacement, what is the new average after one value is replaced?
Statement IThe average of 5 numbers is 20.
Statement IIThe number 15 is replaced by 25.
ExplanationStatement I alone gives old sum = 100 but not the replacement. Statement II alone lacks the count and old average. Together: new sum = 100 − 15 + 25 = 110, new average = 110 / 5 = 22. -
DS2 Easy
During an interview practice question, does the average increase after replacement?
Statement IThe value removed from the set is 30.
Statement IIThe value put in its place is 45.
ExplanationThe average rises if and only if the new value exceeds the old value. Statement I or II alone is incomplete; together 45 > 30, so the average increases.
-
DS3 Medium
A placement set asks for the original value that was replaced. What is the replaced number x?
Statement IThe average of 7 numbers is 16.
Statement IIReplacing x with 28 raises the average to 18.
ExplanationFrom I: old sum = 112. From II with I: new sum = 7 × 18 = 126, so 28 − x = 14 → x = 14. Both statements are required. -
DS4 Medium
An aptitude worksheet asks for the new average after a correction-style replacement. What is the new average?
Statement IThe average of 10 numbers is 45.
Statement IIThe number 70 is replaced by 50.
ExplanationTogether: old sum = 450, new sum = 450 − 70 + 50 = 430, new average = 430 / 10 = 43. Each statement alone is insufficient.