Total Assassination

$0<\frac{a}{b}<1 \implies$

$\begin{cases} 0<a<b \\ a+b=400\\ \end{cases}$

$\implies 0<a<200$

Also,

$gcd(a,b)=1 \implies gcd(a,400-a)=gcd(a,400)=1 \implies$

$\begin{cases} gcd(a,400)=1\\ 0<a<200\\ \end{cases}$

$\implies$

$\begin{cases} gcd(a,200)=1\\ 0<a<200\\ \end{cases}$

So, we need to calculate the Euler totient function for $200$

$\phi(200)=80$

<?php
$c = 0;
for($a=1;$a<=399;$a++){
for($b=$a+1;$b<=399;$b++){
if($a+$b==400 && gcd($a,$b)==1){
$c++;
}
}
}
echo $c; //prints 80

function gcd($a,$b) {
return ($a % $b) ? gcd($b,$a % $b) : $b;
}
?>