number of integers between 1 and 1000 (both inclusive) which are divisible by either of 10, 15 or 25 is

number of integers between 1 and 1000 (both inclusive) which are divisible by either of 10, 15 or 25 is

number of integers between 1 and 1000 divisible by 10 is 100

number of integers between 1 and 1000 divisible by 15 is 66

number of integers between 1 and 1000 divisible by 25 is 40

number of integers between 1 and 1000 divisible by 10 and 15 is multiples of 30 and is 30

number of integers between 1 and 1000 divisible by 10 and 25 is multiples of 50 and is 20

number of integers between 1 and 1000 divisible by 25 and 15 is multiples of 75 and is 13

number of integers between 1 and 1000 divisible by 10,15 and 25 is multiples of 150 and is 9

so,

number of integers between 1 and 1000 (both inclusive) which are divisible by either of 10, 15 or 25 is

= 100+66+40-30-20-13+9 = 152

number of integers between 1 and 1000 divisible by 10 is 100

number of integers between 1 and 1000 divisible by 15 is 66

number of integers between 1 and 1000 divisible by 25 is 40
number of integers between 1 and 1000 divisible by 10 and 15 is multiples of 30 and is 33

number of integers between 1 and 1000 divisible by 10 and 25 is multiples of 50 and is 20
 

number of integers between 1 and 1000 divisible by 25 and 15 is multiples of 75 and is 13
number of integers between 1 and 1000 divisible by 10,15 and 25 is multiples of 150 and is 6
 

number of integers between 1 and 1000 (both inclusive) which are divisible by either of 10, 15 or 25 is

100+66+40=206

now 206-(33+20+13)+6

=146 Ans.