Question

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

• A. $10$
• B. $14$
• C. $13$
• D. $7$

Answer 1

Answer: (A)

$10$

Let the speed of rickshaw and bus be $x$ and $y$ km/hr.

$speed=\frac{distance}{time}\Rightarrow time=\frac{distance}{speed}$

As the total distance traveled by her is 14 km.

$\therefore$ Distance traveled by bus $=14-$ Distance traveled by rickshaw

Case I:-

She takes half an hour if she travels 2 km by rickshaw, and the remaining distance by bus.

$\therefore \underset{\text{time taken by rickshaw}}{\frac{2}{x}}+\underset{\text{time taken by bus}}{\frac{12}{y}}=\underset{\text{total time taken}\left(given\right)}{\frac{1}{2}}⟶eq.\left(1\right)$

Case II:-

If she travels 4 km by rickshaw and the remaining distance by bus, she takes 9 minutes longer.

total time taken by her $=\frac{1}{2}+\frac{9}{60}=\frac{39}{60}hr$

$\therefore \underset{\text{time taken by rickshaw}}{\frac{4}{x}}+\underset{\text{time taken by bus}}{\frac{10}{y}}=\underset{\text{total time taken}\left(given\right)}{\frac{39}{60}}⟶eq.\left(2\right)$

On solving eq. 1 and 2, we get

$x=10$ km/hr

$y=40$ km/hr

Hence, speed of rickshaw is $10$ km/hr.