Question

Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half an hour if she travels 2 km by rickshaw, and the remaining distance by bus. On the other hand, if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9 minutes longer. Find the speed of the rickshaw and the bus in km/hr respectively.

• A. 10 km/hr, 30 km/hr
• B. 10 km/hr, 40 km/hr
• C. 30 km/hr, 10 km/hr
• D. 40 km/hr, 10 km/hr

Answer 1

The correct option is B 10 km/hr, 40 km/hr

Let the speed of the rickshaw be x km/min and the speed of the bus be y km/min.
Since $\text{Time}=\frac{\text{Distance}}{\text{Speed}}$ ,
$\frac{2}{x}+\frac{12}{y}=30$
$\frac{4}{x}+\frac{10}{y}=39$
(where $x\ne 0,y\ne 0)$
Substituting $\frac{1}{x}$ as u and $\frac{1}{y}$ as v, we get
$2u+12v=30$ …(1)
$4u+10v=39$ …(2)
Multiplying equation (1) by 2, we get $4u+24v=60$ …(3)
Subtracting equation (2) from equation (3), we get $14v=21$ $\Rightarrow v=\frac{3}{2}$
Putting $v=\frac{3}{2}$ in equation (1), we get $2u+12\times \frac{3}{2}=30$
$\Rightarrow 2u=30-18$
$\Rightarrow u=\frac{12}{2}=6$

$\therefore x=\frac{1}{6}\text{km/min and}y=\frac{2}{3}\text{km/min}$.
To get the speed in km/hr, we multiply each speed with 60, since 1 hr = 60 min.
$x=\frac{1}{6}\times 60=10\text{km/hr}$
$y=\frac{2}{3}\times 60=40\text{km/hr}$