Subject: General Aptitude · Chapter: Races and Games of Skill · Exam: 2009 · Marks: · Difficulty:
In a 400 m race, $A$ gives $B$ a start of 5 seconds and beats him by 15 m. In another race of 400 m, $\underline{A}$ beats $B$ by $7 \frac{1}{7}$ seconds. Their respective speeds are
(a)6 m/sec, 7 m/sec
(b)5 m/sec, 7 m/sec
(c)8 m/sec, 7 m/sec
(d)9 m/sec, 7 m/sec
Answer
Answer (as printed): C
Explanation
Suppose $A$ covers 400 m in $t$ sec. Then, $B$ covers 385 m in $(t+5)$ sec. $$\therefore B \text { covers } 400 \mathrm{m} \text { in }\left\{\frac{(t+5)}{385} \times 400\right\} \sec =\frac{80(t+5)}{77} \mathrm{sec} \text {. }$$ Also, $B$ covers 400 m in $\left(t+7 \frac{1}{7}\right) \mathrm{sec}=\frac{(7 t+50)}{7} \mathrm{sec}$. $$\therefore \frac{80(t+5)}{77}=\frac{7 t+50}{7} \Rightarrow 80(t+5)=11(7 t+50)$$ $\Rightarrow(80 t-77 t)=(550-400) \Rightarrow 3 t=150 \Rightarrow t=50$. ∴ A's speed = $$\frac{400}{50} \mathrm{m} / \mathrm{sec}=8 \mathrm{m} / \mathrm{sec}, B \text { 's speed }=\frac{385}{55} \mathrm{m} / \mathrm{sec}=7 \mathrm{m} / \mathrm{sec} .$$