Question

A walks around a circular field at the rate of \[1\] round per hour while B runs around it at the rate of \[6\] rounds per hour. They start in the same direction from the point at \[7.30a.m.\] They shall first cross each other at:
A. \[7.42a.m.\]
B. \[7.48a.m.\]
C. \[8.10a.m.\]
D. \[8.30a.m.\]

Answer 1

Hint: We are provided that Speed of A is \[1\] round per hour and that of B is \[6\] round per hour. We have found the time when they shall cross each other.
We also know that Both A and B move in the same direction so they will meet each other only when there is a difference of round between the two. So, we need to then find out the relative speed of A and B.
Relative speed can be obtained by subtraction speed of A from a speed of B.

Complete step-by-step answer:
A round a circular field at the rate of \[1\] round per hour.
Speed of A\[ = \] \[1\] round per hour
B runs around the circular field at the rate of \[6\] round per hour
So, speed of B\[ = \] \[6\] rounds per hour
Since they move in the same direction, they will meet each other only if there will be a difference in their rounds covered.
So, Relative speed of A and B = Speed of B\[ - \]Speed of A
\[ = 6 - 1\]
\[ = \]\[5\] rounds per hour
Now, we will use this relative speed to calculate the time taken to complete rounds
Time is taken to complete one round\[ = \]\[\dfrac{1}{5}hours\]
We will change hours in minutes
We know that
\[1hour = 60\min \]
\[\dfrac{1}{5}hour = \dfrac{1}{5} \times 60\]
\[ = 12\min \]
So, they will meet after \[12\] min from the time when they started
Therefore, the exact time when they meet is \[7:30 + 12 = 7:42\]a.m.
So, Option (A) is the correct answer.
Hence, they cross each other at \[7:42a.m\]

So, the correct answer is “Option A”.

Note: While solving this question we should keep in mind the direction in which A and B are moving. In this question, they are moving in the same direction so we need to find the relative speed of A and B.
Also, we need to take care of units of time. In this question we are given time in min so we need to convert hour to min, simply leaving an hour and calculating it can create an error in the answer.
Always apply the formula which is asked in this.