Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.

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#### Solution

Solution:

Numbers which are divisible by both 2 and 5 are the numbers which are

divisible by 10.

Thus we need to find the number of natural numbers between 101 and 999 which are divisible by 10.

The first number between 101 and 999 which is divisible by 10 is 110 And the last number between 101 and 999 which is divisible by 10 is 990 Using the formula for arithmetic progression

where first term ( a ) = 110, last term ( T_{n} ) = 990 and difference (d) =10

T_{n}=a+(n-1)d

990=110+(n-1)d

880=(n-1)10

n-1=88

n=89

Hence there are 89 natural numbers between 101 and 999 which are divisible by both 2 and 5.

Concept: Sum of First n Terms of an AP

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