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 :
A. 36 metres
B. 48 metres
C. 60 metres
D. 72 metres
Answer: Option B
Solution(By Examveda Team)
Let A finish the race of $$x$$ metresB 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
$$\eqalign{ & \Rightarrow \frac{{x - 12}}{{x - 18}} = \frac{x}{{x - 8}} \cr & \Rightarrow \left( {x - 12} \right)\left( {x - 8} \right) = x\left( {x - 18} \right) \cr & \Rightarrow {x^2} - 20x + 96 = {x^2} - 18x \cr & \Rightarrow 96 = 2x \cr & \Rightarrow x = 48\,\,\text{metres} \cr} $$
Related Questions on Speed Time and Distance
A. 48 min.
B. 60 min.
C. 42 min.
D. 62 min.
E. 66 min.
A. 262.4 km
B. 260 km
C. 283.33 km
D. 275 km
E. None of these
A. 4 hours
B. 4 hours 30 min.
C. 4 hours 45 min.
D. 5 hours
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