Correct Answer - Option 1 : 20
Given:
The batting average of a cricketer is 60 runs per innings
In the next 6 innings, he scores 480 runs and thereby increases his batting average by 6 runs
Formula used:
Average = sum of the observation/number of observation
Calculation:
Let the number of innings played by him till the last match = p
His number of innings before 6 innings = p – 6
So, his runs scored when his number of total innings is
⇒ 60 = p/(p – 6)
⇒ p = (p – 6) × 60
And runs scored finally = (p – 6) × 60 + 480
According to the question,
His final average per innings after those last 6 innings = 60 + 6 = 66
Thus his runs = 66p
⇒ (p – 6) × 60 + 480 = 66p
⇒ 60p – 360 + 480 = 66p
⇒ 66p – 60p = 480 – 360
⇒ 6p = 120
⇒ p = 20
∴ Total number of innings played by him till the last match is 20.
Alternate method:
Average runs in the last 6 innings = 480/6 = 80 runs
We see this average is more than the old average by 80 – 60 = 20
Hence, his excess runs in the last 6 innings = 20 × 6 = 120
Excess of average after those 6 innings = 6
So, the number of total innings played by him till the last match = 120/6 = 20
∴ The total number of innings played by him till the last match is 20
