A cricketer has a certain average for 9 innings. In the tenth innings, the score is 100 runs, thereby increasing his average by 8 runs. His new average is:

The problem can be solved in the following steps:

Step 1: Let's assume the average of the first 9 innings is 'x' runs.

Step 2: So, the total runs scored in the 9 innings is 9x.

Step 3: According to the problem, the cricketer scores 100 runs in the 10th innings and this increases his average by 8 runs. So, the new average is (x+8) runs.

Step 4: The total runs scored in 10 innings is therefore 9x (runs from the first 9 innings) + 100 (runs from the 10th innings).

Step 5: But this total is also equal to the new average (x+8) times the number of innings (10). So, we can set up the equation 9x + 100 = 10(x + 8).

Step 6: Solving this equation gives x = 36.

Step 7: Therefore, the new average after the 10th innings is x + 8 = 36 + 8 = 44 runs.