Three runners A, B and C run a race, with runner A finishing 12 metres ahead of runner B and 18 metres ahead of runner C, in another race of same type runner B finished 8 metres ahead of runner C. Each runner travels the entire distance at a constant speed. The length of the race is :

Answer: Option B

Let A finish the race of $$x$$ metres
B finish the race of = $$x$$ - 12
C finish the race of = $$x$$ - 18 ..... (i)
In another race of B & C
B finish race of = $$x$$
C finish race of = $$x$$ - 8 ..... (ii)
Ratio of speeds of B & C
$$\begin{array}{rl}& \Rightarrow \frac{x-12}{x-18}=\frac{x}{x-8}\\ & \Rightarrow \left(x-12\right)\left(x-8\right)=x\left(x-18\right)\\ & \Rightarrow x^2-20x+96=x^2-18x\\ & \Rightarrow 96=2x\\ & \Rightarrow x=48\text{metres}\end{array}$$