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Question

A batsman by scoring 68 runs in his 20th inning improves his average by 2 runs. His average for all 20 innings is

A
28
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B
30
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C
32
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D
34
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Solution

The correct option is A 30
let the 19 innings runs be a1,a2,...,a19

let the average of 19 innings be ¯x

Therefore, ¯x=a1+a2+...+a1919

a1+a2+...+a19=19¯x -------(1)

Given that 20th inning runs is 68

The average is increased by 2 with the 20th inning runs.

¯x+2=a1+a2+...+a19+a2020

a1+a2+...+a19+68=20¯x+40

a1+a2+...+a19+28=20¯x -------(2)

substituting (1) in (2) we get

19¯x+28=20¯x

¯x=28

Therefore, the 20 innings average is ¯x+2=28+2=30

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