Question

The batting average of a cricket player for 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. Determine his highest score, scored in one innings.

• A. 175
• B. 180
• C. 174
• D. 185

Answer 1

The correct option is C 174

Let the lowest score in one innings be x. Then,
Highest score in an innings = x + 172
Total runs in 40 innings = 40 x 50 = 2000
Total runs in 38 innings = 38 x 48 = 1824
Given, 2000 - {x + (x + 172)} = 1824
$\Rightarrow$ 1828 - 2x = 1824 $\Rightarrow$ 2x = 4 $\Rightarrow$ x = 2
$\therefore$ Highest score = 172 + 2 = 174