Question

Walking \[\dfrac{6}{7}th\]of his usual speed, Sanchit is 12 minutes late. The usual time taken by him to cover that distance.
A. 2 hr
B. 1 hr 12 min
C. 1 hr 15 min
D. 45 min

Answer 1

Hint: We will obtain the relation between new speed of sanchit and usual speed of sanchit from the condition given in the question. Then obtain the relation between usual time taken by time and the new time taken by him by using the speed- distance formula. By further solving, we will get the desired answer.

Formula used:
$Speed=\dfrac{Dis\tan ce}{Time}$

Complete step-by-step answer:
First, let us assume that the usual speed of sanchit is u
And let his new speed be v. So, as per the condition given in the question
$v=\dfrac{6}{7}u\text{ }...........\text{(1)}$
We know that the formula for speed is
$Speed=\dfrac{Dis\tan ce}{Time}$
Which indicates that speed is inversely proportional to time, so we get the relation
New time = $\dfrac{7}{6}$usual time ……….(2)
Now, in the question it is given that walking by new speed he gets 12 minutes late. That is he takes 12 minutes more than the usual time to travel the same distance.
So, we can write the equation as
$\begin{align}
  & \text{New time - usual time = 12 min} \\
 & \Rightarrow \text{New time - usual time = }\dfrac{1}{5}hr \\
\end{align}$
From equation (2) we can write that
\[\begin{align}
  & \left( \dfrac{7}{6}\text{usual time} \right)-\left( \text{usual time} \right)=\dfrac{1}{5}hr \\
 & \Rightarrow \dfrac{1}{6}\text{usual time=}\dfrac{1}{5}hr \\
 & \Rightarrow \text{usual time=}\dfrac{6}{5}hr \\
 & \Rightarrow \text{usual time=}\dfrac{6}{5}\times 60\min \text{ }..............\text{(converting hours to minutes)} \\
 & \Rightarrow \text{usual time= 72 min } \\
 & \therefore \text{usual time= 1hr 12min }..............\text{(converting minutes into h}ours) \\
\end{align}\]
Thus, the usual time taken by him to cover that distance is 1hr 12 min

So, the correct answer is “Option B”.

Additional Information: In some questions displacement is given so we modify our speed formula as $velocity=\dfrac{Displacement}{time}$

Note: One must remember to convert time values in one unit, either in hour or minutes as per the question. The conversion values are given below :
1 hr = 60 minutes
1 minute= 60 seconds
Check in which unit the answer is given and convert the value accordingly.