Question

The battting 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. The highest score of the player is

• A. $165$ runs
• B. $170$ runs
• C. $172$ runs
• D. $174$ runs

Answer 1

The correct option is D $174$ runs

Let the highest score be 'x' and lowest score be 'y'

According to the question

$x-y=\mathrm{172.......}\left(i\right)$

$x+y=50\times 40-48\times 38=\mathrm{176......}\left(ii\right)$

Adding (i) and (ii)

$x-y+x+y=172+176$

$2x=348$

$x=174$

Putting in (i)

$174-y=172$

$y=2$

Therefore the highest score is 174