CAT Quant Practice Problems

Question: Consider three circular parks of equal size with centers at A1, A2, and A3 respectively. The parks touch each other at the edge as shown in the figure (not drawn to scale). There are three paths formed by the triangles A1A2A3, B1B2B3, and C1C2C3, , as shown. Three sprinters A, B, and C begin running from points A1, B1 and C1 respectively. Each sprinter traverses her respective triangular path clockwise and returns to her starting point.

Let the radius of each circular park be r, and the distances to be traversed by the sprinters A, B and C be a, b and c respectively. Which of the following is true?

Sprinter A traverses distances A1A2, A2A3, and A3A1 at an average speed of 20, 30 and 15 respectively. B traverses her entire path at a uniform speed of \(\left( {10\sqrt 3 + 20} \right).\) C traverses distances C1C2, C2C3 and C3C1 at an average speeds of \(\frac{{40}}{3}\left( {\sqrt 3 + 1} \right),\frac{{40}}{3}\left( {\sqrt 3 + 1} \right)\) and 120 respectively. All speeds are in the same unit. Where would B and C be respectively when A finishes her sprint?

  1. B1, C1
  2. B3, C
  3. B1, C3
  4. B1, Somewhere between C3 and C1

Correct Option:3

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