A batsman has a certain average of runs for 16 innings. In the 17th inning he…
2023
A batsman has a certain average of runs for 16 innings. In the 17th inning he makes a score of 85 runs, thus increasing his average by 3 runs. What is the average of the batsman after 17 innings?
Answer: B. 37 — ConceptAn average equals the total of all observations divided by the number of observations. If n observations have average a, their total is na. After…
- A.
35
- B.
37
- C.
45
- D.
40
Show answer & explanation
Correct answer: B
Concept
An average equals the total of all observations divided by the number of observations.
If n observations have average a, their total is na. After adding a value x, the new average is (na + x)/(n + 1).
Application
Let the average after the first 16 innings be a runs. Their total is 16a runs.
The 17th score is 85 and the average rises by 3, so the new average is a + 3. Hence, (16a + 85)/17 = a + 3.
Multiplying by 17 gives 16a + 85 = 17a + 51, so a = 34.
Therefore, the average after 17 innings is 34 + 3 = 37 runs.
Cross-check
The first 16 innings total 16 × 34 = 544 runs. Including 85 gives 629 runs, and 629 ÷ 17 = 37, exactly 3 more than 34.
Result: The required average is 37 runs.