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A,B,C are three persons on a circular road in random positions.they start moving simultaneously clockwise with constant speeds such that after some time t, all the three persons A,B,C are at the intial positions of B,C and A respectively (none of them completed a full circle lap during the time t), if  A,B, C can cover the entire circular track in 15,20 and 20 minutes respectively ,the t (in sec) can be

A)360

B)180

C)90

D)540
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2 Answers

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Let speed of A, B and C is Sa, Sb, and Sc m/sec respectively, circumference of Circular Track is x metres.

Suppose initial position of A,B and C is 


A reaches B with speed Sa in time t, distance covered by A is Da=Sa*t

B reaches C with speed Sb in time t, distance covered by B is Db=Sb*t

C reaches A with speed Sc in time t, distance covered by C is Dc=Sc*t

A can cover distance x in 15 min, Speed of a (Sa) = x/(15*60)  m/sec

B can cover distance x in 20 min, Speed of a (Sb) = x/(20*60)  m/sec

C can cover distance x in 20 min, Speed of a (Sc) = x/(20*60)  m/sec

It is clear from the figure that sum of the individual distances of A, B and C is equal to circumference of circular track which is x.

Da +Db +Dc =x

Substituing all the values in above equation we get

$(x.t/900) + (x.t/1200) +(x.t/1200) = x \\ \ t= 360 sec$

Hence option A) is correct

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