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A batsman has certain average till his first 15 innings. After those 15 innings, he scores 65 and 75 runs in consecutive innings and thereby increases his average by 5 runs. What was his average till 15 innings?

A batsman has certain average till his first 15 innings. After those 15 innings, he scores 65 and 75 runs in consecutive innings and thereby increases his average by 5 runs. What was his average till 15 innings? Correct Answer 27.5

Let us assume that his average till 15 innings be 'm'

Runs scored by him in 15 innings = 15 × m (∵ Average = Sum of observations/No. of observations)

Then he scores 65 and 75 runs in 16th and 17th innings respectively

∴ New average = m + 5 = (15m + 65 + 75)/17

⇒ m + 5 = (15m + 140) /17

⇒ 17(m + 5) = (15m + 140)

⇒ 17m + 85 = 15m + 140

⇒ 2m = 140 – 85 = 55

⇒ m = 55/2 = 27.5

∴ His average till 15 innings will be 27.5

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