Question

One rickshaw leaves Patna junction for Gandhi Maidan at every $10\,\min $. The distance between Gandhi Maidan and Patna junction is $6\,km$. The rickshaw travels at the speed of $6\,kmh{r^{ - 1}}$. What is the number of rickshaws that a rickshaw puller driving from Gandhi Maidan to Patna junction must be on the route if he starts from Gandhi Maidan simultaneously with one of the rickshaws leaving Patna junction?
(A) $11$
(B) $12$
(C) $5$
(D) $1$

Answer 1

Hint: First we have to determine the time taken by one rickshaw to reach the Gandhi Maidan from Patna junction. For that time interval taken by one rickshaw, then how many rickshaws will start from the Patna junction will be determined by using the given information. Simultaneously the rickshaw starts from the Gandhi Maidan to the Patna junction, so by adding the number of rickshaws from Patna junction to Gandhi Maidan and Gandhi Maidan to Patna junction, the total number of rickshaws can be determined.

Formula Used:
By using the velocity formula and then rearranging this formula, the time is given by,
$t = \dfrac{d}{v}$
Where, $t$ is the time taken by the rickshaw, $d$ is the distance between Gandhi Maidan and Patna junction and $v$ is the velocity or speed of the rickshaw.

Complete step by step answer:
Given that,
The time interval between the rickshaws is $10\,\min $, that means for every $10\,\min $ one rickshaw will start travelling.
The distance between Gandhi Maidan and Patna junction is $6\,km$.
The rickshaw travels at the speed of $6\,kmh{r^{ - 1}}$.
Now,
By using the velocity formula, the time taken is given by,
$t = \dfrac{d}{v}\,.....................\left( 1 \right)$
By substituting the distance and the speed of the rickshaw in the above equation, then
$t = \dfrac{{6\,km}}{{6\,kmh{r^{ - 1}}}}$
On dividing the above equation, then
$t = 1\,hr$
By the given information, every $10\,\min $ one rickshaw will start travelling, so for $1\,hr$ $6$ rickshaws will start travelling from the Patna junction to the Gandhi Maidan.
Simultaneously, $5$ rickshaws will travel on the road from Gandhi Maidan to Patna junction.
So, the total number of rickshaws are $ \Rightarrow 6 + 5 \Rightarrow 11$
Hence, the option (A) is the correct answer.

Note: Here for $1\,hr$ the number of rickshaw will travel on the road is $6$, after the first rickshaw reaches the Gandhi Maidan, the number of rickshaws will travel on the road from Gandhi Maidan to the Patna junction is $5$ rickshaws. Then adding the number of rickshaws from Patna junction to the Gandhi Maidan and Gandhi Maidan to Patna junction, the solution is determined.