First count the sum of all integers between 1 and 1000 inclusive which are multiples of 5.Call it a.

Then count the sum of all integers between 1 and 1000 inclusive which are multiples of 8.Call it b.

Now a+b will have the sum of all integers between 1 and 1000 inclusive which are multiples of 5 and 8, with repetitions. Numbers that are divisible by both 8 and 5 would have occurred in both a and b. Thus 'a+b' has counted multiples of 40 twice. So you will have to subtract the sum of all integers between 1 and 1000 inclusive which are multiples of 40 from 'a+b'.

So the process is easy if you can answer the following questions:

1) How to determine the sum of all integers between 1 and 1000 inclusive which are multiples of 5?

2) How to determine the sum of all integers between 1 and 1000 inclusive which are multiples of 8?

3) How to determine the sum of all integers between 1 and 1000 inclusive which are multiples of 40?