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:

Question: 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:

Solution:
Let A finish the race of x metres
B finish the race of = x - 12 meters.
C finish the race of = x - 18 - - - - - - - - (1)
In another race of B & C
B finish race of = x meters.
C finish race of = x - 8 - - - - - - - - (2)
Ratio of speeds of B & C
(x - 12)/(x - 18) = x/(x - 8)
⇒ (x - 12)(x - 8) = x(x -18)
⇒ x² - 12x - 8x + 96 = x² - 18x
⇒ x^{2 -} 20x + 96 = x² - 18x
⇒ 96 = 2x
∴ x = 48 metres.

∴ The length of the race is 48 meters.