The batting average for 40 innings of a cricket player is 50 runs. His highest score exceeds his lowest score by 172 runs. If these two innings are excluded, the average of the remaining 38 innings is 48 runs. Find out the highest score of the player.
150
174
180
166
Explanation:
Total runs scored by the player in 40 innings = $ 40 \times 50$
Total runs scored by the player in 38 innings after excluding two innings = $ 38 \times 48$
Sum of the scores of the excluded innings = $ 40 \times 50 - 38 \times 48 = 2000 - 1824 = 176$
Given that the scores of the excluded innings differ by 172. Hence lets take
the highest score as x + 172 and lowest score as $x$
Now $x + 172 + x$ = 176
=> 2$x$ = 4
=> $x=\dfrac{4}{2}$ = 2
Highest score = $x$ + 172 = 2 + 172 = 174