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CAT 2005 — QA Question 4

Basics of Mensuration/PrismEasy

A jogging park has two identical circular tracks touching each other, and a rectangular track enclosing the two circles. The edges of the rectangles are tangential to the circles. Two friends, A and B, start jogging simultaneously from the point where one of the circular tracks touches the smaller side of the rectangular track. A jogs along the rectangular track, while B jogs along the two circular tracks in a figure of eight. Approximately, how much faster than A does B have to run, so that they take the same time to return to their starting point?

Answer & solution

  • A

    3.88%

  • B

    4.22%

  • C

    4.44%

  • 4.72%

Solution

​​​​​​​

Let r be the radius of the circular tracks.

Length and breadth of the rectangular track are 4r and 2r respectively.

Length (perimeter) of the rectangular track = 12r

Length of the two circular tracks (figure of eight) = 4πr

If A and B have to reach their starting points at the same time,

 12ra=4πrb
(where a and b are the speeds of A and B respectively)

∴ ba=4π12

⇒ (b-a)a=4π-1212

∴ (b - a) × 100a = 0.047 × 100 = 4.7%

Hence, option (d).

CAT 2005 QA Q4: A jogging park has two identical circular tracks touching each other, and a rectangular track enclosing the tw — Solution | TheCATExam