The average speed of a train is 20% less on the return journey than on the…
2023
The average speed of a train is 20% less on the return journey than on the onward journey . The train halts for half an hour at the destination station before starting on the return journey . If the total time taken for the to and fro journey is 22(1/2) hours , covering a distance of 1000 km , then speed of the train on the return journey is
- A.
55 km/hr
- B.
40 km/hr
- C.
50 km/hr
- D.
60 km/hr
Attempted by 3 students.
Show answer & explanation
Correct answer: B
Answer: Approximately 40.91 km/hr
Let the onward speed be x km/hr. Then the return speed = 0.8x km/hr.
Total distance covered to and fro = 1000 km, so each way is 500 km. The train halts for 0.5 hour. The total time given is 22.5 hours, so total travel time (excluding halt) = 22.5 − 0.5 = 22 hours.
Travel time equation: 500/x + 500/(0.8x) = 22.
Combine terms: 500(1 + 1/0.8)/x = 22. Since 1/0.8 = 1.25, 1 + 1.25 = 2.25, so 500 × 2.25 / x = 22 ⇒ 1125/x = 22.
Solve for x: x = 1125/22 ≈ 51.13636 km/hr. Therefore the return speed = 0.8x ≈ 0.8 × 51.13636 ≈ 40.90909 km/hr.
Note: The exact return speed is about 40.91 km/hr. None of the provided options matches this value exactly; the option "40 km/hr" is close but not the precise answer. The solution image provided earlier contains algebraic errors and led to an incorrect exact value of 40 km/hr, so it has been replaced with this step-by-step derivation.