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.
We know that $time=\frac{distance}{speed}$
$\frac{2}{x}+\frac{12}{y}=30$
$\frac{4}{x}+\frac{10}{y}=39$

Substituting $\frac{1}{x}$ as u and $\frac{1}{y}$ as v (where $x\ne 0,y\ne 0)$, we get
$2u+12v=30\dots \left(1\right)$
$4u+10v=39\dots \left(2\right)$

On multiplying equation (1) by 2, we get $4u+24v=60\dots \left(3\right)$
On 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, $x=\frac{1}{6}km/minandy=\frac{2}{3}km/min$.
To get the speed in km/hr, we multiply each speed with 60
[$\because$ 1 hr = 60 min]
$x=\frac{1}{6}\times 60=10km/hr$
$y=\frac{2}{3}\times 60=40km/hr$

Therefore, the speed of the rickshaw is 10 km/hr and the speed of the bus is 40 km/hr.