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After 11 innings, the average score per innings of a batsman is 52. After 13 innings, the average increased to 54. If the batsman scored 16 more runs in the 13th innings than the previous innings, then how many runs did he score in the 12th innings?

After 11 innings, the average score per innings of a batsman is 52. After 13 innings, the average increased to 54. If the batsman scored 16 more runs in the 13th innings than the previous innings, then how many runs did he score in the 12th innings? Correct Answer 57

Given:

The average score after 11 innings = 52

The average score after 13 innings = 54

The Batsman scored 16 more runs in the 13th innings than the previous innings

Formula used:

Average = Sum of observations/Number of observations

Calculation:

Let the score of batsman in 12th innings be x

Let the score of batsman in 13th innings more than the previous innings be (x + 16)

The average score after 11 innings = (52 × 11) = 572

The average score after 13 innings = (54 × 13) = 702

According to the question

⇒ (572 + x + x + 16) = 702

⇒ (588 + 2x) = 702

⇒ 2x = (702 – 588)

⇒ 2x = 114

⇒ x = (114/2)

⇒ x = 57

∴ He scored 57 runs in his 12th innings

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