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Two trains start from pt. A to pt. B in the same direction and move back from the pt. B to pt. A. The distance between A to B is 90 km. The ratio of the speed of the trains is 4 : 5 respectively. The faster train covers the one-way distance in 3 hrs. At what distance away from pt. B, both trains will meet for the first time?
1. 70 km
2. 36 km
3. 72 km
4. 50 km
5. 40 km

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Correct Answer - Option 5 : 40 km

Given:

Distance between pt. A and pt. B = 90 km

Time taken by faster train to cover the distance = 3 hrs

Ratio of speed = 4 : 5

Concept:

In these types of questions, we find the speed of both the trains and then find the distance cover in 3 hrs and then we use the relative speed concept.

Formula:

Relative speed = S1 + S2 (when direction is opposite)

Distance = speed × time

Calculation:

Let the speed of the faster and slower trains be 5x and 4x respectively

⇒ 90 = 5x × 3

⇒ x = 6

Speed of faster train = 5x = 5 × 6 = 30 km/hr

Speed of slower train = 4x = 4 × 6 = 24 km/hr

Time of meeting = 90/(30 + 24) = 1.67 hour = 100 min

∴ Distance from point B = 24 × 100/60 = 40 km

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