In IPL, Dhoni scored an average of 120 runs per match in the first 3 matches and an average of 140 runs per match in the last four matches. What is Dhoni’s average runs for the first match and the last two matches if his average runs per match for all the five-match is 122 and the total number of matches is 5?

In IPL, Dhoni scored an average of 120 runs per match in the first 3 matches and an average of 140 runs per match in the last four matches. What is Dhoni’s average runs for the first match and the last two matches if his average runs per match for all the five-match is 122 and the total number of matches is 5? Correct Answer 100

Given:

Dhoni scored an average in the first 3 match = 120 runs per match

Dhoni scored an average in the last 4 match = 140 runs per match

Average runs per match for all the five matches = 122

Formula Used:

Average = (Total run)/Number of innings

Calculation:

Let the scores in the 5 exams be denoted by M1, M2, M3, M4, and M5

Dhoni’s average score in the first 3 matches = 120

M1 + M2 + M3 = 120 × 3 = 360

⇒ M1 + M2 + M3 = 360      ----(i)

Average in last 4 match = 140

M2 + M3 + M4 + M5 = 140 × 4

⇒ M2 + M3 + M4 + M5 = 560      ----(ii)

Average of all matches = 122 × 5

⇒ M1 + M2 + M3 + M4 + M5 = 610      ----(iii)

Subtracting (ii) form (iii), we get

⇒ M1 = (610 – 560) = 50

Subtracting (i) from (ii), we get

M4 + M5 – M1 = (560 – 360)

⇒ M4 + M5 = (200 + 50) = 250

Now, M1 + M4 + M5 = (50 + 250) = 300

Required average = 300 / 3

⇒ Required average = 100