Ans is option (B)
Let the speed of the slower bicyclist be $x$ miles per hour. Then the speed of faster bicyclist would be $x+5$ miles per hour.
Using the concept of relative motion here, let’s keep the slower bicyclist at rest. Then the faster bicyclist would be traveling towards the slower bicyclist with a speed of $x+5-(-x)=2x+5$ miles per hour.
Now, the faster bicyclist travels $50$ miles in $2$ hours.
$\therefore$ $2=\frac{50}{2x+5}$ ($\because$ time $=$ distance/ speed)
$\Rightarrow$ $x=10$ miles per hour.
So, the speed of the faster bicyclist is, $10+5=15$ miles per hour.