CMAT 2015 Solved Question Paper

(a) Since, Arman beats Bhuvan by 100 m.
∴ Ratio of speeds of Arman and Bhuvan = 1000: 900 = 10:9
Let speed of Arman be 10x m/s and speed of Bhuvan be 9x m/s.
Distance covered = 1 km = 1000 m
Time taken by Arman = $\frac{1000}{10\mathit{x}}\mathit{s}$
Time taken by Bhuvan = $\frac{1000}{9\mathit{x}}\mathit{s}$
According to the question,
$$$\frac{1000}{10\mathit{x}}+10=\frac{1000}{9\mathit{x}}$
⇒ $\frac{1000}{10\mathit{x}}-\frac{1000}{9\mathit{x}}=-10$
⇒ 1000$\left(\frac{1}{9\mathit{x}}-\frac{1}{10\mathit{x}}\right)=10$
⇒ 1000$\left(\frac{10-9}{90\mathit{x}}\right)$ = 10
⇒ $\frac{1000}{90\mathit{x}}$ = 10
⇒ 1000 = 10 × (90x)
∴ x = $\frac{1000}{900}=\frac{10}{9}$
Required time = $\frac{1000}{10}\times \frac{9}{10}\mathit{s}$ = $\frac{9000}{100}$ = 90 s = 1 min 30s