A and B start from the same point and in the same direction at 7 am to walk around a rectangular field 400 m × 300 m. A and B walk at the rate of 3 km/hr and 2.5 km/hr respectively. How many times shall they cross each other if they continue to walk till 12.30 pm ?

Answer: Option B

Perimeter of the field
= 2(400 + 300) m
= 1400 m
= 1.4 km
Since A and B move in the same direction, so they will first meet each other when there is a difference of one round i.e., 1.4 km between the two.
Relative speed of A and B = (3 - 2.5) km = 0.5 km/hr
Time take to cover 1.4 km at this speed :
$$\begin{array}{rl}& =\left(\frac{1.4}{0.5}\right)\text{ hr}\\ & =2\frac{4}{5}\text{ hr}\\ & =2\text{ hr 48 min}\end{array}$$
So, they shall first cross each other at 9.48 am
And again 2 hr 48 min after 9.48 am i,e., 12.36 pm
Thus, till 12.30 pm they will cross each other once.