The new average of 8 numbers after removing the 5th number is 36.25.
Given:
The average of 9 numbers is 35.
The average of the first 5 numbers is 32.
The average of the last 5 numbers is 37.
We need to find the new average of 8 numbers if the 5th number is removed.
Let's represent the sum of the 9 numbers as 'S'. We can express the given information using the following equations:
S/9 = 35
(S - 5x)/5 = 32
(S - 5x)/5 = 37
Where 'x' represents the 5th number.
Solving for 'x', we get:
x = 5
Now, we can find the sum of the remaining 8 numbers:
S - 5x = (35 * 9) - (5 * 5) = 290
Finally, we can calculate the new average of 8 numbers:
(S - 5x)/8 = 290/8 = 36.25
Therefore, the new average of 8 numbers after removing the 5th number is 36.25.