Question

Ted and his friends Ned and Red are running a race. Ted on track A, Ned on B and Red on track C. The radius of track A is 14 m. For a fair race, the initial separation between Ted and Ned is 22 m. Find the initial separation between Ned and Red if the radius of the tracks increases uniformly.

• A. 22 m
• B. 44 m
• C. 28 m
• D. 48 m

Answer 1

The correct option is A

22 m

The circumference of track A = 2$\pi$ r = 2 $\times$ $\left(\frac{22}{7}\right)$ $\times$ 14 = 88 m

The circumference of track B = circumference of track A + 22 m = (88 + 22) m = 110 m

Let the radius of track B be r’. So, circumference of track B = 2$\pi$ r’

2 $\pi$ r’ = 110 m

2 $\times$ $\left(\frac{22}{7}\right)$ $\times$ r’ = 110

r’ = 17.5 m

Increase in radius = (17.5 - 14) = 3.5 m

So, radius of track C = r” =(17.5 + 3.5) m = 21 m

Circumference of track C = 2 $\pi$ r” = 2 $\times$ $\left(\frac{22}{7}\right)$ $\times$ 21 = 132 m

But Red has to run for only 88 m. So, separation between Ned and Ted = (132 – 88) m = 44 m

And separation between Ned and Red = (44 – 22) m = 22 m