A and B started walking simultaneously in the same direction from a po

Question

A and B started walking simultaneously in the same direction from a point on a circular track. The time taken by them to meet for the first time was five times the time that they would have taken to meet for the first time had they started walking in opposite directions. If A's speed was less than that of B's, and the speed of A was 12 km/hr, what was the speed of B?

A. 18 m/s
B. 12 m/s
C. 8 m/s
D. 5 m/s
E. 4 m/s

Are You Up For the Challenge: 700 Level Questions

A. 18 m/s
B. 12 m/s
C. 8 m/s
D. 5 m/s
E. 4 m/s

Are You Up For the Challenge: 700 Level Questions

GMATinsight · Accepted Answer

Suppose their speeds are b and a

Relative speed in same direction = b-a
Relative speed in Opposite direction = b+a
Let, length fo circular track = D

Time = \frac{Distance }{ Speed}

\frac{D}{(b-a)} = \frac{5D}{(b+a)}

i.e. a+b = 5b - 5a

i.e. 6a = 4b

i.e. b = 1.5a

a = 12 kmph
i.e. b = 18 kmph

i.e. b = 18*1000/3600 = 5 m/s

Answer: Option D

Archit3110 · Answer

let speed of A = a and speed of B = b
total distance = x

when in same direction total time would be
x/a-b and
when in opposite direction total time ; x/a+b
given a = 12 kmph or say 12 * 5/18 ; 3.3 mps
so
x/b-a = 5x/a+b
we get
a+b=5b-5a
6a=4b
3a=2b
3*3.3=2b
b= 5 m/s ;
OPTION D

GMATWhizTeam · Answer

Solution 
 • Let us assume that the speed of B and the length of the circular track be b m/s and d meters, respectively.
• The speed of A  = 12 km/hr = 12*\frac{5}{18 }= \frac{10}{3}  m/s
• If A and B moves in the same direction their relative speed  = b – \frac{10}{3}  m/s
• And if A and B moves in the opposite direction then their relative speed  = b + \frac{10}{3}  m/s
• Now, according to the question stem, 
 o  \frac{d}{b – \frac{10}{3}} = 5*\frac{d}{b + \frac{10}{3}} ⟹\frac{3b + 10}{3b -10} = 5 ⟹3b + 10 = 15b – 50 ⟹ 12b = 60 ⟹ b = 5  m/s  
Thus, the correct answer is  Option D.

CrackverbalGMAT · Answer

In case of a question on Circular tracks, there are two important concepts that can be tested:
1) Time taken to meet for the first time (anywhere on the track)
2) Time taken to meet for the first time at the starting point.

This question is on the first concept. To find the time, we use this equation:

Time taken to meet for the first time =  \frac{Length of track }{ Relative speed}

Speed of A = 12 km/hr. Since the answer is required to be given in m/s, 12 km/hr will have to be converted to m/s, which can be done by multiplying 12 by  \frac{5}{18} .

12 *  \frac{5}{18}  =  \frac{10 }{ 3}  m/s.

Let the speed of B be x metres per second.

When both of them are travelling in the same direction, their relative speed = (x- \frac{10}{3} ) =  \frac{(3x – 10)}{ 3}  metres per second (notice how the smallest answer option is more than 10/3, therefore we subtract 10/3 from x)

When both of them are travelling in the opposite direction, their relative speed = (x +  \frac{10}{3} ) =  \frac{(3x + 10) }{3}  metres per second.

Time taken to meet for the first time, when moving in the same direction =  \frac{L }{ (3x-10)/3}  =  \frac{3L }{ (3x-10)}  seconds (assume the length of the circular track is L metres)

Time taken to meet for the first time, when moving in the opposite direction =  \frac{L }{ (3x+10)/3}  =  \frac{3L }{ (3x+10)}  seconds

It’s given that  \frac{3L }{ (3x-10)} = 5 * \frac{3L }{ 3x + 10} .

Simplifying the equation above and solving for x, we get x = 5 metres per second. 
The correct answer option is D.

Hope that helps!
Aravind B T

samarpan.g28 · Answer

Given, speed of A=12 kmph. Let, speed of B=x kmph. Also given, x>12.
Relative speed in same direction 12+x kmph, in opposite direction x-12 kmph (since x>12).
We know, s=d/t or t=d/s.
From the question,  d/(x-12)  =  5d/(12+x) . Solving, we get x=18 kmph.
Therefore, (18*1000)/3600 = 5 m/s. Option (D) is correct.

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A and B started walking simultaneously in the same direction from a po

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