Question

find the number of natural number between 50 and 500 which when divided by 5 leaves remainder 2​

Answer 1

To find:

The number of natural number between 50 and 500 which when divided by 5 leaves remainder 2​

Solution:

Such numbers will be:

$52, 57, 62, 67, ......, 497$

We can see that it is an AP (Arithmetic progression).

Which has:

First term, $a = 52$

Common difference, d (Second term - First Term = Third term - Second term ) = 57-52 = 5

d = 5

We have to find n for $a_n = 497$

First of all, let us have a look at the formula for general term ($n^{th}$ term) of an AP:

$a_n=a+(n-1)d$

$\Rightarrow 497 = 52 + (n-1)\times 5\\\Rightarrow 497 - 52 = 5n-5\\\Rightarrow 445+5= 5n\\\Rightarrow 450= 5n\\\Rightarrow n =90$

So, the answer is: There are a total of 90 numbers between 50 and 500 which have remainder 2 when divided by 5.