Question

The batting average for 40 innings of a cricket player is 50 runs. His highest score exceeds his lowest score by 120 runs. If these two innings are not included, the average of the remaining 38 innings is 48 runs. The lowest score of the players is:

1. 30
2. 28
3. 31
4. 29

Answer 1

Correct Answer - Option 2 : 28

Given:

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

His highest score exceeds his lowest score by 120 runs

If two innings are not included, the average of the remaining 38 innings is 48 runs

Formula used:

Average = sum of the observation/number of observation

Calculation:

Average = Sum of the 40 innings runs/total innings

⇒ 50 = Sum of the 40 innings runs /40

⇒ Sum of the 40 innings runs = 2000

According to question,

If two innings are not included

So, sum of 38 innings is 48

⇒ 48 = Sum of 38 innings/38

⇒ Sum of 38 innings run = 38 × 48

⇒ Sum of 38 innings run = 1824

So, two innings run = Sum of the 40 innings run – Sum of 38 innings run

⇒ Two innings run = 2000 – 1824

⇒ Two innings run = 176

Let minimum run be Q

So, maximum run is Q + 120

⇒ Q + Q + 120 = 176

⇒ 2Q = 176 – 120

⇒ 2Q = 56

⇒ Q = 28

∴The lowest score of the players is 28