Management Aptitude Test Sep 2011 Paper

(1) Let speed of train and taxi are x km/h and y km/h respectively.
Then, using the formula,
$\frac{\mathrm{Distance}}{\mathrm{Speed}}$ = Time, we get
$\frac{300}{\mathit{x}}+\frac{200}{\mathit{y}}=\frac{11}{2}$ ⇒ $\frac{3}{\mathit{x}}+\frac{2}{\mathit{y}}=\frac{11}{200}$
$\frac{36}{\mathit{x}}+\frac{24}{\mathit{y}}=\frac{132}{200}=\frac{33}{50}$ .......(i)
and
$\frac{360}{\mathit{x}}+\frac{240}{\mathit{y}}=\frac{28}{5}$
⇒ $\frac{36}{\mathit{x}}+\frac{24}{\mathit{y}}=\frac{28}{50}$ .......(ii)
subtracting eq. (ii) from Eq. (i), we get
$\frac{10}{\mathit{x}}-\frac{33}{50}-\frac{28}{50}=\frac{5}{50}=\frac{1}{10}$
⇒ x = 100 km/h