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In a circular race of 900m length, A and B start with speeds 27 km/hr and 36 km/hr starting at the same time from the same point. When will they meet for the first time at the starting point when running in opposite direction?
  • a)
    2 min 50 sec
  • b)
    6 min
  • c)
    5 min 40 sec
  • d)
    7 min
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?
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In a circular race of 900m length, A and B start with speeds 27 km/hr ...
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In a circular race of 900m length, A and B start with speeds 27 km/hr ...
Given:
● Length of the race = 900m
● Speed of A = 27 km/hr
●Speed of B = 36 km/hr

To find:
Time taken by A and B to meet for the first time at the starting point when running in opposite direction.

Solution:
When A and B run in opposite directions, their relative speed = Speed of A + Speed of B

Relative speed = (27 + 36) km/hr = 63 km/hr

Converting km/hr to m/s by multiplying with 5/18, we get:
Relative speed = 63 x 5/18 m/s = 175/6 m/s

Let the time taken by A and B to meet for the first time be 't' seconds.
● Distance covered by A in 't' seconds = 27 x 5/18 x t = 15/2 t meters
● Distance covered by B in 't' seconds = 36 x 5/18 x t = 10t meters

Total distance covered by A and B in 't' seconds = (15/2 t + 10t) meters

As they meet at the starting point, the total distance covered by them should be equal to the length of the race, i.e., 900m.

Therefore, (15/2 t + 10t) = 900
Simplifying the above equation, we get:
35t = 1800
t = 1800/35 seconds

Converting seconds to minutes, we get:
t = (1800/35) x 1/60 minutes
t = 5.14 minutes (approx)

Therefore, A and B will meet for the first time at the starting point after 5.14 minutes (approx) or 6 minutes (approx). Hence, option B is the correct answer.
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Community Answer
In a circular race of 900m length, A and B start with speeds 27 km/hr ...
B
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In a circular race of 900m length, A and B start with speeds 27 km/hr and 36 km/hr starting at the same time from the same point. When will they meet for the first time at the starting point when running in opposite direction?a)2 min 50 secb)6 minc)5 min 40 secd)7 mine)None of theseCorrect answer is option 'B'. Can you explain this answer?
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