Time taken using inverse ratio of speeds – UGC NET Question

For a fixed distance, time is inversely proportional to speed. Let the distance between P and Q be d. The onward time is d/60 and the return time is d/40. Their ratio is (d/60):(d/40) = 1/60:1/40 = 40:60, which simplifies to 2:3. Hence, the ratio of onward time to return time is 2:3.

Option A:
Option A, 3:2, reverses the correct ratio. This would imply that the onward journey at higher speed takes more time than the return journey at lower speed, which contradicts the basic principle of inverse proportionality between time and speed for the same distance.

Option B:
Option B, 4:5, does not match the fractional comparison 1/60:1/40. If we attempted to equate 4:5 to 40:60, they would not simplify to the same reduced form. Therefore 4:5 is not aligned with the correct calculation.

Option C:
Option C is correct because it results from cancelling the common factor d and then simplifying the fraction 40:60. This ratio correctly reflects that the car spends less time on the onward trip at 60 km/h than on the return trip at 40 km/h by a factor of 2 to 3.

Option D:
Option D, 5:4, suggests only a mild difference between the times and in the wrong direction. It cannot be derived from the exact speeds given and leads to an incorrect relationship between the onward and return travel times.