A train running at 5/12 of its original speed reached a place in 18 hours. How…
2023
A train running at 5/12 of its original speed reached a place in 18 hours. How much time (in hours) could be saved if the train would have run at its original speed?
- A.
7.5
- B.
10.5
- C.
15
- D.
18
Attempted by 1 students.
Show answer & explanation
Correct answer: B
Concept
For a fixed distance, speed and time are inversely proportional: Speed × Time = Distance = constant. So if the speed is scaled by a factor k (with the same distance), the time taken is scaled by the reciprocal factor 1/k.
Step-by-step application
Let the original (full) speed be S and the original (full-speed) time be T. The train actually runs at (5/12)S and takes 18 hours to cover the same distance.
Since distance is the same in both cases: S × T = (5/12)S × 18.
Cancelling S from both sides: T = (5/12) × 18 = 7.5 hours — this is the time the train would have taken running at its original speed.
Time saved = actual time taken − original-speed time = 18 − 7.5 = 10.5 hours.
Cross-check
Cross-check: the ratio of actual time to original time is 18 / 7.5 = 2.4 = 12/5, which is exactly the reciprocal of the speed ratio 5/12 — confirming the inverse speed–time relationship holds and the answer 10.5 hours is consistent.
