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Question:

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?

Explanation:

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,

$\frac{12 r}{a} = \frac{4 π r}{b}$
(where a and b are the speeds of A and B respectively)

∴ $\frac{b}{a} = \frac{4 π}{12}$

⇒ $\frac{(b - a)}{a} = \frac{4 π - 12}{12}$

∴ (b - a) × $\frac{100}{a}$ = 0.047 × 100 = 4.7%

Hence, option (d).