Three runners A,B and C run a race, with runner A finishing 12 meters ahead of runner B and 18 meters ahead of runner C, while runner B finishes 8 meters ahead of runner C. Each runner travels the entire distance at a constant speed. The length of the race is

Let the total length of races be L meters.

A finishes 12 meters ahead of B.

$$\Rightarrow$$ B : A = (L - 12) : L     -------- (1)

A finishes 18 meters ahead of C.

$$\Rightarrow$$ A : C = L : (L - 18)     --------- (2)

B finishes 8 meters ahead of C.

$$\Rightarrow$$ B : C = L : (L - 8)      ---------- (3)

Multiplying equation (1) and equation (2), we get,

$$\Rightarrow$$ B : C = (L - 12) : (L - 18)

Equating the above equation with equation (3), we get,

$$\Rightarrow$$ L : (L - 8) = (L - 12) : (L - 18)

$$\Rightarrow$$ L $$\times$$ (L - 18) = (L - 12) $$\times$$ (L - 8)

$$\Rightarrow$$ L$$^2$$ - 18L = L$$^2$$ - 20L + 96

$$\Rightarrow$$ 2L = 96

$$\Rightarrow$$ L = 48 meters

Hence, option B is the correct choice.