Question

Two persons A and B are standing diametrically opposite on a circular track of radius 3.5 units. They start running in an opposite direction on the circular track and their speeds are four units/min and seven units/min, respectively. On meeting each other, they take rest for half a min and then start running with twice the original speed. In five min, how many times will they take rest together?

• A. 6 times
• B. 7 times
• C. 10 times
• D. None of these

Answer 1

The correct option is D None of these

As r $=\frac{7}{2}$ units
Circumference $2\pi r=2\times \frac{22}{7}\times \frac{7}{2}=22units$
First, they will cover 11 units with relative speed = 11 units/min
Time = $\frac{11}{11}=1min$
Now, they will cover 22 units with twice their relative Speed. Hence,
Time
$\begin{array}{ccc}Firstmeetingrest& Secondmeetingrest& Thirdmeetingrest\\ 1min\frac{1}{2}min& 1min\frac{1}{2}min& \frac{1}{2}min\frac{1}{2}min\\ Fourthmeetingrest& Fifthmeetingrest& \\ \frac{1}{4}min\frac{1}{2}& \frac{1}{8}min\frac{1}{2}min& \end{array}$
Therefore, in 5 min, they will take rest five times.
Hence, option (d) is the answer.