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A and B start from the same point and in the same direction at 7:00 am to walk around a rectangular field 400m x 300m. A and B walk at the rate of 3km/h and 2.5km/h respectively. How many times shall they cross each other, if they continue to walk till 12: 30 pm?
Options:
A .  Not even once
B .  Once
C .  Twice
D .  Thrice
Answer: Option B


Total time for which A and B Travel = 5h 30 min = 5 1/2h (From 7:00am “ 12:30 pm) 
Speed of A = 3km/h 
Therefore, Distance travelled by A in 5 1/2h 
= 3 x 11/2 = 16.5km 
 And the speed of B = 2.5km/h 
Therefore, Distance travelled by B in 5 1/2h = 2.5 x 11/2 = 13.75km 
Therefore in 5 1/2h, 
The difference in distance travelled by A and B is (16.5 - 13.75km.i.e...2.75km 
The total extra distance needs to be travelled by one in order to cross the other by at least once. 
= Length of path around the field 
Perimeter of the rectangle =2(l+b)= 2(400+300) =1400m =1.4km 
Hence A may cross more than once they may need at least 1.4x2 =2.8km 
the difference between themselves but the difference is 2.75km, they can only once cross each other.



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