A batsman makes a score of 79 runs in the 18th inning and thus increases his average by 2. Find his average after 18th inning.

Correct option is B

Given:

The batsman scores 79 runs in the 18th inning.

His average increases by 2 runs after the 18th inning.

Formula Used:

​​​Total score after n innings = n $$\times$$​Average score after n innings

Solution:

Let the average score after 17 innings be A.

The total score for the first 17 innings will be $$17 \times A.$$​​

After the 18th inning, his average increases by 2, so the new average is A + 2.

The total score after 18 innings is $$18 \times (A + 2).$$​​

Total score after 18 innings = Total score after 17 innings + 79

​$$18 \times (A + 2) = 17 \times A + 79$$​​

18A + 36 = 17A + 79

18A - 17A = 79 - 36

A = 43

Thus, the average after 17 innings was 43.

The new average after the 18th inning is:

A + 2 = 43 + 2 = 45

The average after the 18th inning is 45.

Thus, the correct option is (b) 45

Alternate Method:

Let the average of 18 innings = 18 A

So, the average of 17 innings =  17(A -2)

Since, score score of 18^th innings = 79

=> 17(A - 2) + 79 = 18 A

=>17 A - 34 + 79 = 18A

=> A = 45