There are 32 consecutive natural numbers. The average of the first 13 numbers is X. What is the average of the next 19 numbers?

The average of the first 13 numbers is X.

As we know that the average is the middle number of the series. Because we know that numbers are consecutive.

So in the first 13 numbers, 7th number will be the middle as well as the average of these numbers which is equal to 'X'.

13th number = X+6

14th number = X+7

Similarly 32nd number = X+25

So in the next 19 numbers, the first number will be (X+7) and the last one will be (X+25).

Average of the next 19 numbers = $$\frac{first\ number+last\ number}{2}$$

= $$\frac{(X+7)+(X+25)}{2}$$

= $$\frac{2X+32}{2}$$

= (X+16)