Multiples of 5 and 7

Numbers are less than 350 means 350 is not included.
N(5) means multiples of 5.
N(7) means multiples of 7.
N(5&7) means multiples of 5&7 both.
N(5)=350/5=70.
N(7)=350/7=50.
N(5&7)=350/35=10.
N(5 or 7)=N(5)+N(7)-N(5&7)=70+50-10=110.
but 350 is also not included means 110-1=109

(350/5-1) + (350/7-1) - (350/5x7-1) = 69 + 49 - 9 = 109

Every 1 out of 5 of mulitipe of 7 is also a multiple of 5

x = ( 350/5) + (( 350/7) * 4/5 ) - 1

x = 70 + ( 50 * ( 4/5) ) - 1 = 70 + 40 - 1 = 109

numbers are up to 349 Numbers divisible by 5 = 349/5 = 69 and 349/7 = 49

number divisible by 5 and 7 are 69 + 46 = 118 but these numbers contain number divisible by 5× 7 u.e. LCM of 5 and 7 which are common to both such numbers are 349/35 = 9 are to be subtracted.

so required numbers = 118 – 9 = 109

350/5=70 and 350/7=50 and 350/(5x7)=10 but as 350 is not included thus 1 is subtracted from each 69,49,9 and as there are 9 no.s which are divisible by both 5 and 7 but they are counted twice so 69+49-9=109