Sum of 6 no. =23*6= 138
Sum of 5 no. = 20*5=100
Excluded no. = 138-100
=38.

Problem:
The mean of six numbers is 23. If one of the numbers is excluded, the mean of the remaining numbers is 20. Find the excluded number.

Solution:
To find the excluded number, we can follow these steps:

Step 1: Calculate the sum of the six numbers.
Step 2: Calculate the sum of the remaining five numbers after excluding one number.
Step 3: Find the difference between the two sums.
Step 4: Divide the difference by 5 to find the value of the excluded number.

Step 1: Calculate the sum of the six numbers:
Let's assume the six numbers as a, b, c, d, e, and f.

The sum of the six numbers can be represented as:
Sum = a + b + c + d + e + f

Given that the mean of the six numbers is 23, we can write the equation:
Sum/6 = 23

Multiplying both sides by 6, we get:
Sum = 138

Step 2: Calculate the sum of the remaining five numbers:
Now, let's exclude one number from the six numbers and consider the remaining five numbers as a, b, c, d, and e.

The sum of the remaining five numbers can be represented as:
Sum' = a + b + c + d + e

Given that the mean of the remaining numbers is 20, we can write the equation:
Sum'/5 = 20

Multiplying both sides by 5, we get:
Sum' = 100

Step 3: Find the difference between the two sums:
The difference between the sum of the six numbers and the sum of the remaining five numbers can be represented as:
Difference = Sum - Sum'

Substituting the values of Sum and Sum' obtained from Step 1 and Step 2 respectively, we have:
Difference = 138 - 100
Difference = 38

Step 4: Divide the difference by 5 to find the value of the excluded number:
To find the value of the excluded number, we divide the difference by 5:
Excluded number = Difference / 5
Excluded number = 38 / 5
Excluded number ≈ 7.6

Conclusion:
The excluded number is approximately 7.6.