To find the mean of the 32 numbers, we can use the concept of weighted averages.

Given:

1. The mean of 10 of the numbers is 15.
2. The mean of 20 of the numbers is 11.
3. The last two numbers are 10.

Let's denote:

First 10 Natural numbers are:- 1,2,3,4,5,6,7,8,9,10

Mean = Sum of all numbers/ total number of observations

        = 1+2+3+4+5+6+7+8+9+10 / 10 

        = 55/ 10 

        = 5.5

Therefore, 5.5 is the mean of first 10 natural numbers

in this question mean is already given and we know that:-

           mean = sum of total numbers / total number of observations

             15 = 2+6+7+a / 4

             15*4 = 15+a

               60 = 15+a

               60-15 = a

                 a= 45

now we have found the value of a=45, we will put this value in second series:-

                mean = sum of all numbers / total number of observations

                50 = 6+18+1+45(value of a) + b / 5

                50*5 = 70 + b

                250 = 70 + b

                 b = 250 - 70

                 b = 180

The mean of the first n natural numbers can be calculated using the formula for the arithmetic mean: