Question : The batting average for a cricket player's 40 innings is 50 runs. His highest score in an innings exceeds his lowest score by 172 runs. If these two innings are excluded, the average of the remaining 38 innings is 48 runs. The highest score for the player is:
Option 1: 165 runs
Option 2: 170 runs
Option 3: 172 runs
Option 4: 174 runs
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Correct Answer: 174 runs
Solution :
Let the lowest score in one inning be $x$ runs.
Highest score in an inning = ($x$ + 172) runs
The average of 40 innings = 50 runs
⇒ Total runs in 40 innings = 40 × 50 = 2000
The average of the remaining 38 innings = 48 runs
⇒ Total runs in 38 innings = 38 × 48 = 1824
⇒ 2000 – [$x$ + ($x$ + 172)] = 1824
⇒ 1828 – 2$x$ = 1824
⇒ 2$x$ = 4
⇒ $x$ = 2
Highest score = 172 + 2 = 174
Hence, the correct answer is 174 runs.
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