Question

There are two concentric circular track of radii 100m and 102m, respectively . A runs on the inner track and goes once round in 1 min 30 sec while B runs on the outer track in 1 min 32 sec. Who runs faster?

• A. A
• B. B
• C. Cannot be determined
• D. None of these

Answer 1

The Correct Option is B

First let us take out the circumferences of both circles.
Radius of inner circle = 100 m
\(\therefore\)Circumference of the inner track= 2\(\pi r\)
                                               = 2\(\times\)3.14\(\times\)100
                                               = 628 m
Radius of outer track= 102 m
So, Circumference of outer track=2\(\pi r\) = 2\(\times\)3.14\(\times\)102 = 753.6 m
Time taken by A = 1 min 30 sec = 90 sec
Time taken by B = 1 min 32 sec = 92 sec
Speed of A = Distance covered by A/ Time taken
                \(=\frac{628}{90}\)

                \(=\frac{6.98m}{s}\)
Speed of B = Distance covered by B /time taken
               \(=\frac{753.6}{92}\)

               \(=\frac{8.19m}{s}\)
Speed of A is smaller than the speed of B.
So, B runs faster.
So the correct option is (B)