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 :
Correct Answer: 48 metres
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
$$\eqalign{ & \Rightarrow \frac{{x - 12}}{{x - 18}} = \frac{x}{{x - 8}} \cr & \Rightarrow \left( {x - 12} \right)\left( {x - 8} \right) = x\left( {x - 18} \right) \cr & \Rightarrow {x^2} - 20x + 96 = {x^2} - 18x \cr & \Rightarrow 96 = 2x \cr & \Rightarrow x = 48\,\,\text{metres} \cr} $$
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
$$\eqalign{ & \Rightarrow \frac{{x - 12}}{{x - 18}} = \frac{x}{{x - 8}} \cr & \Rightarrow \left( {x - 12} \right)\left( {x - 8} \right) = x\left( {x - 18} \right) \cr & \Rightarrow {x^2} - 20x + 96 = {x^2} - 18x \cr & \Rightarrow 96 = 2x \cr & \Rightarrow x = 48\,\,\text{metres} \cr} $$