The sum of all natural numbers less than 201 which are divisible by either 5 or 6 but not by both is?

Natural numbers less than 201 and divisible by 5 are 5, 10, . . .200. Here, 5+200 = 10+195  . . = 100+105. Hence, there are 40/2 = 20 pairs totalling 205.

Sum of all natural numbers less than 201 divisible by 5 is 20*205 = 4100

Similarly, natural numbers less than 201 and divisible by 6 are 6, 12, . . .  198. 6+198= 12+192= . . . = 96+108  and 102. Hence, there are $$\lfloor201/6 /2 \rfloor$$ = 16 such pairs and 102.

Sum of all natural numbers less than 201, divisible by 6 is 16*204 + 102 = 3366

Similarly, Sum of all natural numbers divisible by both 5 and 6 is 6*210/2 = 630. These numbers have been summed in both the above totals. Hence, we need to deduct 2 times 630.

So, required total is 4100+3366-2*630 = 6206