Question

A long-distance runner runs 9 laps of a 400-meter track every day. His timings (in min) for four consecutive days are 88, 96, 89 and 87 respectively. On an average, how many meters/minute does the runner cover?
A. 17.78
B. 90
C. 40
D. None of these.

Answer 1

Hint: Calculate the total length of 9 laps of a 400-meter track. Multiply this by 4 to get the total distance ran in four days.
Calculate the total time (in minutes) taken by him in all the four days together.
Use the fact that the distance and time are directly proportional to each other, to calculate the distance covered per (1) minute.

Complete step-by-step answer:
The total distance covered by the runner in 1 day = 9 laps of 400 meters each = $ 9\times 400 $ meters.
The total distance covered by him in 4 days = $ 4\times (9\times 400) $ meters.
Total time taken by him in all four days = $ 88+96+89+87 $ minutes = 360 minutes.
Since the distance and time are directly proportional to each other, we can multiply / divide both of them by the same number, without changing their rate (ratio).
  $ 4\times (9\times 400) $ meters in 360 minutes
Let's divide both of them by 360 to get at 1 minute as the value of the time.
⇒ $ \dfrac{4\times (9\times 400)}{360} $ meters in $ \dfrac{3600}{360} $ minutes
⇒ 40 meters in 1 minute.
Therefore, the runner covers 40 meters per minute.
So, the correct answer is “Option C”.

Note: Ratio is derived from Latin, literally ‘reckoning’, from rat- ‘reckoned’, e.g. ratify; and it means the same as rate in mathematics.
Direct proportion: If two quantities are directly proportional to each other, then if the value of one of the quantities becomes n times, the value of the other also becomes n times.
Inverse/Indirect proportion: If two quantities are inversely proportional to each other, then if the value of one of the quantities becomes n times, the value of the other quantity becomes $ \dfrac{1}{n} $ times.