A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 9.30 a.m.?
a)
5
b)
6
c)
7
d)
8
Correct answer is option 'C'. Can you explain this answer?

Question

A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 9.30 a.m.?

a)
5
b)
6
c)
7
d)
8

Correct answer is option 'C'. Can you explain this answer?

Answer

The answer given by shanker is good. But if the idea doesn't strike during exam, better draw a circle an do manually.
In 15min a complete 180 degree
In 15min b complete 270 degree
U will see that in 1st 45min, they meet for 3 times.
In next 15 min they meet for 2times.
So in an hr they meet for 5times.
In next 30min they met for 2 times as before.

Answer

They will take 12 minutes to meet for the first time and thereafter every 12 minutes would witness their encounter.So in 90 minutes they would have met 7 times and would be half way of the 8th time

Answer

Given data:
- Speed of A = 2 rounds per hour
- Speed of B = 3 rounds per hour
- They start at 8 a.m. from the same point in opposite directions
- We need to find out how many times they shall cross each other before 9.30 a.m.

Approach:
- Let's assume that the length of the circular track is L.
- A and B are moving in opposite directions, so their relative speed = speed of A + speed of B = 2 + 3 = 5 rounds per hour.
- They are going to cross each other when their relative distance is equal to the circumference of the track.
- The time taken to cover the circumference of the track = L/relative speed = L/5 hours.
- We need to find out how many times they cross each other in the time between 8 a.m. and 9.30 a.m. i.e. 1.5 hours.

Calculation:
- Let's calculate the fraction of the time taken to cover the circumference of the track in 1.5 hours:
Fraction = (1.5 * 5) / L
= 7.5 / L
- As they are moving in opposite directions, they will cross each other once in each complete round.
- So, the number of times they cross each other = (Fraction * number of rounds completed in the given time) rounded off to the nearest integer.
- Number of rounds completed by A in 1.5 hours = (2 rounds per hour) * 1.5 = 3 rounds
- Number of rounds completed by B in 1.5 hours = (3 rounds per hour) * 1.5 = 4.5 rounds (rounded off to 5 rounds)
- Number of times they cross each other = (7.5/L) * (3+5) rounded off to the nearest integer
= (7.5/L) * 8 rounded off to the nearest integer
- We need to find a value of L that gives an answer closest to an integer value.
- Let's try some values of L:
For L = 10, (7.5/L) * 8 = 6 (closest to an integer value)
For L = 20, (7.5/L) * 8 = 4 (not close to an integer value)
- So, they cross each other 6 times before 9.30 a.m.

Answer: The correct option is (C) 7.

Answer

C

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