Question

3. How many natural numbers between 200 and 400
are there which are divisible by
I. Both 4 and 5 ?
II. 4 or 5 or 8 or 10 ?​

Answer 1

Answer:

option b is ur answer

Step-by-step explanation:

hope it helps

Answer 2

Answer:

I. 9

II. 79

Step-by-step explanation:

I. The term which are divisible by 8 should also be divisible by 4 and the term which divisible by 10 must be divisible by 5.

So we need to find all the numbers between 200 and 400(excluding 200 and 400) which are divisible 4 and 5.

Now,Total number of natural numbers between 200 and 400 divisible by 4 and 5 = Total number of factors of 4 + Total number of factors of 5-Total number of factors of 20

Now

All numbers between 200 and 400 from an AP with common difference 4 and first term 204 and last term = 396

Let total number of terms be n

Thus, tn =a+(n−1)d

396=204+(n−1)4

(n−1)4=192

n=49

II. Again numbers divisible by 5 from an AP with common difference 5 and first term as 205 and last term as 395

Thus number of term = {(an−a)/d}+1={(395−205)/5}+1=39

Similarly for numbers of terms divisible by 20 are ={(380−220)/20}+1=9

Thus total number of factors of 4 and 5 =49+39−9=79