# 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 ru

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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. What is total number of innings played by him till the last match?

1. 20
2. 22
3. 18
4. 24

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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