A batsman in his 13th inning makes a score of 97 runs, thereby increasing his average score by 5. What is his average score after the 13th inning?

A batsman in his 13th inning makes a score of 97 runs, thereby increasing his average score by 5. What is his average score after the 13th inning?

1. 77
2. 67
3. 37
4. 57

Sol:

A batsman in his 13th inning makes a score of 97 runs, thereby increasing his average score by 5.

Old average × old number + something = New average × new number

Let his old average (i.e. average till 12th innings) be ‘x’ ⇒ New average is ‘x + 5’ [∵ Average increased by 5] 

∴ x × 12 + 97 = (x + 5) × 13 

⇒ 12x + 97 = 13x + 65 

⇒ x = 32 

∴ New Average = x + 5 = 32 + 5 = 37