Question

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Answer 1

Question :

A batsman makes a score of 148 in his 29th innings and therefore increases his average by 4. His average after the 29th inning 36 runs

Answer :

Let the Average in 28th innings be 'x'

We know that

Sum of observations = Average × No. of observations

So, Sum of runs in 28th innings = 28x

Batsman scores 148 in 29th innings

Sum of runs in 29th innings = 28x + 148

Given :

Average in 29th innings increases his average by 4.

⇒ Average in 29th innings = Average in 28th innings + 4

⇒ Sum of runs / No. of innings = x + 4

⇒ ( 28x + 148 ) / 29 = x + 4

⇒ 28x + 148 = 29x + 116

⇒ 148 - 116 = 29x - 28x

⇒ 32 = x

⇒ x = 32

Average in 28th innings = x = 32 runs

Average in 29th innings = x + 4 = 32 + 4 = 36 runs

Therefore his average in 29th innings is 36 runs.

Answer 2

Given -

Score of Batsman in 29th inning = 148 runs

After 29th inning his average score increases by 4 runs

To Find -

Average score of Batsman after 29th inning .

Solution -

Let's assume that the average score of the batsman of 28 innings = x runs .

↳ As we know that according to the formula for average .

Total runs in 28 innings = 28 × x

↳ Total runs in 28 innings = 28x runs

↳Runs made in 29th inning = 148 runs

Total runs scored in 29 innings all together = runs scored in 28 innings + runs scored in 29th inning .

↳ Runs scored in 28 innings = 28x

↳ Runs scored in 29th inning= 148

↳ Total runs scored = 28x + 148 .

→ Now it is given that in 29th inning the average score of batsman will increased by 4 runs .

↳As average run up to 28 inning = x

↳ After increase of 4 runs average score will = x +4

$\implies \: \frac{28x \: + \: 148}{29} \: = \: x + 4$

↳ 28x + 148 = 29( x+4 )

↳ 28x + 148 = 29 x + 116

↳ 29x - 28x = 148 - 116

↳ x = 32.

↳ Average score is increased by 4 = x+4 = 36 runs

So the average score of the batsman after 29th inning will be 36 runs