Question

The average score of a cricketer for 20 matches is 52 runs. His highest score is more than his lowest score by 120 runs. If these two innings are excluded, the average of the remaining 18 matches is 50 runs. The highest score of the player is
1. 130
2. 125
3. 135
4. 150

Answer 1

Correct Answer - Option 1 : 130

Given

The average score of a cricketer for 20 matches is 52 runs. His highest score is more than its lowest score by 120 runs. If these two innings are excluded, the average of the remaining 18 matches is 50 runs. 

Concept used

Average

Calculation

Total runs scored in 20 mathces is 52 runs

⇒ Sum = 20 × 52 = 1040 runs

Average of remaining 18 matches is 50 runs

⇒ Sum = 18 × 50 = 900 runs

H - L = 120 (Given)      ----(i)

H + L = 1040 − 900

H + L = 140      ----(ii)

Solving the avove two equations

⇒ Highest = \(\frac{{120\ +\ 140}}{2} = 130\)

⇒ Lowest = 140 − 130 = 10

Highest score = 130 runs.

∴ The highest score of the player is 130 runs.

H - L = 120 (Given)      ----(i)

Some time from Eqn 1, candidates infer that highest score is 120 which is incorrect.