Question : The batting average for 30 innings of a cricket player is 40 runs. His highest score exceeds his lowest score by 100 runs. If these two innings are not included, the average of the remaining 28 innings is 38 runs. The lowest score of the player is:
Option 1: 15
Option 2: 18
Option 3: 20
Option 4: 12
Correct Answer: 18
Solution :
Given:
The batting average of a cricket player for 30 innings is 40 runs.
Total runs in 30 innings = 30 × 40 = 1200
Let the lowest and the highest scores be $x$ and $(100+x)$, respectively.
The average score of the remaining 28 innings is 38 runs.
Total runs in 28 innings = 28 × 38 = 1064
The sum of the lowest and the highest scores = 1200 – 1064 = 136
According to the question,
$x + (100 + x) = 136$
$⇒ 2x + 100 = 136$
$⇒ 2x = 36$
$\therefore x = 18$
Hence, the correct answer is 18.
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