The average of runs recorded by 8 players is 40. If the average of the runs by…
2025
The average of runs recorded by 8 players is 40. If the average of the runs by the first five players is 39, and that of the last four players is 34, what is the number of runs recorded by the fifth player?
- A.
16
- B.
11
- C.
14
- D.
20
Show answer & explanation
Correct answer: B
Concept: For a group of n members, Sum = Average × n. When two overlapping subgroups share one common member, adding the two subgroup sums double-counts that member; subtracting the sum of the full group from this combined total isolates exactly the runs of the overlapping member.
Total runs for all 8 players = 8 × 40 = 320.
Sum of runs for the first five players = 5 × 39 = 195.
Sum of runs for the last four players = 4 × 34 = 136.
The fifth player belongs to both groups, so 195 + 136 = 331 counts that player's runs twice within the total of 320.
Runs of the fifth player = (195 + 136) − 320 = 331 − 320 = 11.
Cross-check: With the fifth player scoring 11, the remaining four players (1st–4th) sum to 195 − 11 = 184, and the last three (6th–8th) sum to 136 − 11 = 125. Total = 184 + 11 + 125 = 320, matching 8 × 40 = 320.