When B and C run over the course together, B wins by 15 metres

=> when B runs x metre, C run $\left(x-15\right)$ metre

$\text{=> when B runs 1 metre, C run }\dfrac{x-15}{x}\text{ metre}$

$\text{=> when B runs $\left(x-15\right)$ metre, C run }\dfrac{x-15}{x} \times (x-15) = \dfrac{(x-15)^2}{x}\text{ metre}$

$\text{i.e., }(x-29) = \dfrac{(x-15)^2}{x}$

$\Rightarrow x^2 - 29x = x^2 - 30x + 225$

$\Rightarrow - 29x = - 30x + 225 $

$\Rightarrow x = 225$