Solution

Given:• Two runners, P and Q, competed in a race of 400 m

• P ran at a constant speed of 5 strides in every 2 seconds, covering 10 m in that span

o Hence, in 2 seconds P covered 10 m

Or, speed of P = \(\frac{10}{2}\) m/s = 5 m/s

• Q started the race at a constant speed

• Q covered 4 m in every stride

• After running for 1 minute, Q increased its speed by 1 stride per second

• Q finished the race, taking the same time as P

To find:• The initial speed of Q, in kph

Approach and Working: • As the race distance is 400 m and speed of P is 5 m/s,

o Time taken by P to finish the race = \(\frac{400}{5}\) secs = 80 seconds

• Given that the time taken by P and Q is same, Q also takes 80 seconds to finish the race

• Let us assume that in the initial 60 seconds, Q took x strides per second

o Therefore, in the last 20 seconds, Q took (x + 1) strides per second

• As Q covers 4 m in every stride, the total distance covered by Q = 4 [60x +20(x + 1)] m

Or, 4 [60x + 20 (x + 1)] = 400

Or, 60x + 20x + 20 = 100

Or, 80x = 80

Or, x = 1 stride/sec

• Given that Q covered 4 m in every stride, the initial speed of Q = 4 m/s = 4 * \(\frac{18}{5}\) kph = \(\frac{72}{5}\) kph = 14.4 kph

Hence, the correct answer is option E.

Answer: E
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