Subject: General Aptitude · Chapter: Races and Games of Skill · Exam: 2016 · Marks: · Difficulty:
A runs $1 \frac{2}{3}$ times as fast as B. If A gives B a start of 80m, how far must the winning post from the starting point be so that A and B might reach it at the same time?
(a)200m
(b)300m
(c)270m
(d)160m
Answer
Answer (as printed): A
Explanation
Let speed of $\mathrm{B}=a \mathrm{m} / \mathrm{s}$ Speed of $\mathrm{A}=\frac{5}{3} a \mathrm{m} / \mathrm{s}$ Let $x$ be the distance $=\frac{x \times 3}{5 a}=\frac{x-80}{a}$ $$\begin{aligned} & \Rightarrow 3 x=5 x-400 \quad \Rightarrow 2 x=400 \\ & \Rightarrow x=200 \mathrm{m} \end{aligned}$$