Speed ratio from equal distances – UGC NET Question

For the same distance, speed is inversely proportional to time. Let the common distance be d. The first cyclist’s speed is d/4 and the second’s speed is d/6. Their speed ratio is (d/4):(d/6) = 1/4:1/6 = 6:4, which simplifies to 3:2. Thus, the ratio of their speeds is 3:2.

Option A:
Option A, 2:3, corresponds to the ratio of their times, not their speeds. It would imply that the faster cyclist rides more slowly than the slower one, which contradicts the idea that less time for the same distance means higher speed.

Option B:
Option B is correct because it correctly applies the inverse proportionality between speed and time. The cyclist who takes 4 hours must be faster, and the computed ratio 3:2 quantifies exactly how much faster he is than the one who takes 6 hours.

Option C:
Option C, 4:3, might arise from directly comparing 4 and 6 but simplifying incorrectly. However, when we compute speeds rather than times, we get 3:2, not 4:3. Thus 4:3 is not compatible with the relationship between speed and time here.

Option D:
Option D, 5:4, has no clear basis in the given numbers and does not result from any correct manipulation of the times or speeds. It therefore does not represent the true speed ratio.