Subject: General Aptitude · Chapter: Races and Games of Skill · Exam: · Marks: · Difficulty:
In a 100 m race, $A$ beats $B$ by 10 m and $C$ by 13 m. In a race of $180 \mathrm{m}, B$ will beat $C$ by
(a)5.4 m
(b)4.5 m
(c)5 m
(d)6 m
Answer
Answer (as printed): D
Explanation
$A: B=100: 90$ and $A: C=100: 87 \Rightarrow \frac{A}{B}=\frac{100}{90}=\frac{10}{9}$ and $\frac{A}{C}=\frac{100}{87}$ $\Rightarrow \frac{B}{C}=\left(\frac{B}{A} \times \frac{A}{C}\right)=\left(\frac{9}{10} \times \frac{100}{87}\right)=\frac{90}{87}=\frac{90 \times 2}{87 \times 2}=\frac{180}{174}$ $\Rightarrow \mathrm{B}: \mathrm{C}=180: 174$ ⇒ In a 180 m race, B beats C by $(180-174) \mathrm{m}=6 \mathrm{m}$.