Direction : Read the data given below carefully and answer the questions. A…
2020
Direction : Read the data given below carefully and answer the questions.
A train running between four stations i.e. A, B, C & D on Monday and Tuesday. The average speed of train on Monday during whole journey is 50 kmph and average speed of train on Tuesday during whole journey is 62.5 kmph. On Monday train takes one hour less to cover distance between A and B as compare to that of on Tuesday. Train takes equal time to cover distance between B to C on both the given days, while train takes three hours more to cover distance between C and D as compare to that of on Tuesday. The distance between A and B is 40% less than that of between C and D. The distance between B and C is 50% more than that of between A and B.
Note - There is not any halt or stoppage from the station A to D.
Find the difference between the distance from station A to B and from station C to D?
- A.
60 km
- B.
20 km
- C.
80 km
- D.
40 km
- E.
Cannot be determined
Attempted by 1 students.
Show answer & explanation
Correct answer: C
Concept
For a journey covered at a constant average speed over a fixed total distance, total time = total distance / average speed. When the same distance is travelled on two days at different average speeds, the difference in total times equals the sum of the segment-wise time differences. This lets us find the total distance from the overall time gap, and then split it using the given proportional relations between the segment lengths.
Setting up the relations
Distances are the same on both days. A→B = 60% of C→D (it is 40% less), and B→C = 150% of A→B (50% more).
Writing every segment in terms of C→D: A→B = 0.6·CD and B→C = 1.5·(0.6·CD) = 0.9·CD, so the total A→D = 0.6 + 0.9 + 1.0 = 2.5·CD.
Using the time gap
Segment time differences (Monday minus Tuesday): A→B is 1 hour less (−1), B→C is equal (0), C→D is 3 hours more (+3). Net Monday − Tuesday time = −1 + 0 + 3 = +2 hours.
Total time each day = total distance ÷ average speed. So (Total/50) − (Total/62.5) = 2.
1/50 − 1/62.5 = 1/250, hence Total/250 = 2, giving Total distance = 500 km.
Splitting the total
Total = 2.5·CD = 500 ⇒ C→D = 200 km.
A→B = 0.6 × 200 = 120 km; B→C = 0.9 × 200 = 180 km (check: 120 + 180 + 200 = 500 ✓).
Required difference = C→D − A→B = 200 − 120 = 80 km.
Cross-check
Monday total time = 500/50 = 10 h, Tuesday = 500/62.5 = 8 h, and the gap is exactly 2 h, matching the segment constraints (−1 + 0 + 3). The proportions and the time gap together fix every distance uniquely, so the difference is a single definite value.