A batsman scored 84 runs in his 12$$^{th}$$​ innings, thereby improving his average score per innings by 4 runs. What is the average score per innings of the batsman after the 12$$^{th}$$ innings?

Correct option is B

Given:

- Runs scored in 12th innings = 84

- Increase in average after 12th innings = 4 runs

- Let average after 11 innings = x

- Average after 12 innings = x + 4

Formula Used:

Average = Total runs scored / Number of innings

Solution:

Total runs after 11 innings = 11 × x

Total runs after 12 innings = 11 × x + 84

Average after 12 innings = $$\frac{(Total \ runs \ after \ 12 \ innings) }{ 12}$$​ = x + 4

So, $$\frac{(11 × x + 84) }{ 12 }= x + 4$$​​

11 × x + 84 = 12 × (x + 4)

11x + 84 = 12x + 48

84 - 48 = 12x - 11x

36 = x

Average after 12 innings = x + 4 = 36 + 4 = 40 runs

The average score per innings of the batsman after the 12th innings is 40 runs.