Question

Roohi travels 300 km to her home partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.

• A. Speed of train = 80 km/hr, speed of bus = 60 km/hr
• B. Speed of train = 60 km/hr, speed of bus = 80 km/hr
• C. Speed of train = 90 km/hr, speed of bus = 50 km/hr
• D. Speed of train = 50 km/hr, speed of bus = 90 km/hr

Answer 1

The correct option is B Speed of train = 60 km/hr, speed of bus = 80 km/hr

Let the speed of bus be and that of train be y

Now, according to question and using time $=\frac{\text{distance}}{\text{speed}}$

$\Rightarrow \frac{60}{y}+\frac{240}{x}=4\Rightarrow \frac{15}{y}+\frac{60}{x}=1\left(i\right)$

$\Rightarrow \frac{100}{y}+\frac{200}{x}=\frac{25}{6}\Rightarrow \frac{24}{6}+\frac{48}{x}=1\left(ii\right)$

From (i)
$\Rightarrow \frac{1}{x}=\frac{1}{60}(1-\frac{15}{y})$ putting this is eq (ii)

$\Rightarrow \frac{24}{y}+\frac{48}{60}(1-\frac{15}{y})=1$

$\Rightarrow \frac{24}{y}+\frac{4}{5}-\frac{12}{y}=1$

$\Rightarrow \therefore y=60km/hr$

then x = 80 km/hr

Option B is correct.