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CAT 2003 Slot 2 — QA Question 17

2 CirclesEasy
Passage / Data

Answer the following question based on the information given below.

Consider three circular parks of equal size with centres 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.

Sprinter A traverses distances A1A2, A2A3, and A3A1 at average speeds of 20, 30 and 15 respectively. B traverses her entire path at a uniform speed of (103+20). C traverses distances C1C2, C2C3, and C3C1 at average speeds of 403(3+1),403(3+1), and 120 respectively. All speeds are in the same unit. Where would B and C be respectively when A finishes her sprint?

Answer & solution

  • A

    B1, C1

  • B

    B3, C3

  • B1, C3

  • D

    B1, Somewhere between C3, C1

Solution

Time taken by A to travel through distance a (A1A2 + A2A3 + A3A1)

=2r20+2r30+2r15=3r10

Distance travelled by B in the same time,

=3r10×(103+20)=3r(2+3)=b

∴ B travels a full round in the same time as A. Thus, B will be at B1.

For C, time taken to traverse through C1C2

=2r(3+1)403(3+1)=3r20

Time remaining for C = =(310-320)r=3r20

Now, distance travelled by C in this time = 3r20×4032(1+3)=2r(1+3)=C2C3

∴ C will be at C3.

Hence, option (c).

CAT 2003 Slot 2 QA Q17: Sprinter A traverses distances A 1 A 2 , A 2 A 3 , and A 3 A 1 at average speeds of 20, 30 and 15 respectively — Solution | TheCATExam