Question

If sum of three prime no. is $100$ and one of them exceeds other by $36$, then find the largest no.

Answer 1

Let three prime numbers are x, x+36 and y
According to question, we have

$x+x+36+y=100$
$2x+y=64$ .......(1)
All three are prime number, so $2x$ should be a even number.

Also, to get sum $100$ (even number) $y$ should be an even prime number i.e. $2$.
Putting $y=2$, we get
$2x+2=64$
$x=31$