Subject: General Aptitude · Chapter: Races and Games of Skill · Exam: 2012 · Marks: · Difficulty:
In racing over a distance $d$ at uniform speed, A can beat B by 20 metres, B can beat C by 10 metres, and A can beat C by 28 metres. Then d, in metres, is
(a)50
(b)75
(c)100
(d)120
Answer
Answer (as printed): C
Explanation
Let distance $\mathrm{be}=x$ metre A runs $=x$ metre B runs $=(x-20)$ metres. B can beat C by 10 metres C runs $=(x-10)$ metres A can beat by C 28 metres C runs $=(x-28)$ metres B runs $=x-20$ C runs $=\left(\frac{x-10}{x}\right) \times(x-20)$ 'A' can beat C by 28 metre $x-\left[\frac{(x-10)(x-20)}{x}\right]=28$ $$\begin{aligned} x^{2}-x^{2}+30 x & -200=28 x \quad 30 x-200=28 x \\ \Rightarrow 30 x-28 x & =200 \quad 2 x=200 \\ x & =100 \text { metres. } \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.