The batting average of a cricket player for 40 innings is 50 runs. His

1.	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» Answer 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 × 50 = 2000 Total runs in 38 innings = 38 × 48 = 1824 Given, 2000 – {x + (x+ 172)} = 1824 ⇒ 1828 – 2x = 1824 ⇒ 2x = 4 ⇒ x = 2 ∴ Highest score = 172 + 2 = 174.

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»

Answer 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 × 50 = 2000

Total runs in 38 innings = 38 × 48 = 1824

Given, 2000 – {x + (x+ 172)} = 1824

⇒ 1828 – 2x = 1824 ⇒ 2x = 4 ⇒ x = 2

∴ Highest score = 172 + 2 = 174.

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