Find the arithmetic mean of all three digit numbers whose rightmost digit is twice of left most digit - Concept of average of averages

Question

I was able to solve it by listing all the cases from :-

1. 102, 112, ..., 192

2. 204, 214, ..., 294

3. 306, 316,..., 396

4. 408, 418, ..., 498

I added all the 4 AP series and then divided by total 40 terms to arrive at average

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However in the book, there was a method given which seems more efficient but I am not able to understand that:-

In that the author took average of each series separately like :-

1. average of 1st series - 147

2. average of 2nd series - 249

3. average of 3rd series - 351

4. average of 4th series - 453

and then found out the average of these 4 terms

I am not aware of this method of finding out averages, please help me understand this method