Question

A batsman in his 30th innings makes a score of 120 and thereby increase his average by 3.What was the average after 30th innings?

Answer 1

Let x be the average of the first 29th scores

Find the sum of the 29 scores:

Average = x

Sum = 29x

Find the sum of the 30 scores:

Sum of the 29 scores = 29x

30th score = 120

Sum of the 30 scores = 29x + 120

Find the average of the 30 scores:

Sum of the 30 scores = 29x + 120

Average of the 30 scores = (29x + 120) ÷ 30

Solve x:

His average was increased by 3

⇒ x + 3

(29x + 120) ÷ 30 = x + 3

(29x + 120) = 30 (x + 3)

29x + 120 = 30x + 90

x = 120 - 90

x = 30

Find the average of the 30 scores:

Average of the 30 scores = x + 3 = 30 + 3 = 33

Answer: The average is 33