A and B start from the same point and in the same direction at 7 a.m. to walk around a rectangular field 400 m x 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 til

examrobotsa's picture

Submitted by examrobotsa on

Q: 104 (IAS/2004)
A and B start from the same point and in the same direction at 7 a.m. to walk around a rectangular field 400 m x 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 p.m?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,6,15,5,6,4,6

keywords: 

{'rectangular field': [0, 0, 1, 0], 'twice': [3, 0, 1, 0], 'thrice': [3, 1, 3, 1], 'km': [0, 0, 2, 1], 'rate': [2, 3, 13, 20]}

The total time for which A and B walk is from 7 a.m. to 12:30 p.m. which is 5.5 hrs. The speed of A is 3 km/hr and of B is 2.5 km/hr. So, the distance covered by A in 5.5 hours will be 3*5.5 = 16.5 km and the distance covered by B will be 2.5*5.5 = 13.75 km. The perimeter of the rectangular field is 2*(400+300) m = 1400 m = 1.4 km. So, A will complete 16.5/1.4 = 11.78 ~ 11 rounds; similarly, B will complete 13.75/1.4 = 9.82 ~ 9 rounds. The difference between their rounds is 11-9 = 2 times. So, they will cross each other 2 times.

Option 1 `Not even once` and Option 4 `Thrice` are incorrect because they do not align with the calculations. Option 3 `Twice` is the correct answer as per the calculation, but option 2 `Once` is not correct because