A passenger sitting in a train A moving at 90 ~km / h observes another train B moving in the opposite direction for 8 ~s . If the velocity of the train B is 54 ~km / h , then length of train B is:

Motion in A Straight Line PYQ — JEE Main 2023 · 13 Apr · Shift 2 · Q61 with Solution

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Correct answer: D

Given data
- Speed of train $A = 90\,\text{km/h}$
- Speed of train $B = 54\,\text{km/h}$
- Trains are moving in opposite directions
- Time for which passenger observes train $B = 8\,\text{s}$
Relative speed of train $B$ with respect to passenger in train $A$

Since the trains move in opposite directions, $v_{\text{rel}} = 90 + 54 = 144\,\text{km/h}$

Convert into m/s: $144\times \frac{5}{18} = 40\,\text{m/s}$
Interpretation of the observation

A passenger is effectively a point object. If he sees the whole train $B$ pass by in $8\,$ s, then in relative motion, train $B$ covers a distance equal to its own length in this time.

So, $\text{Length of train }B = v_{\text{rel}} \times t$
Calculate the length $L_B = 40 \times 8 = 320\,\text{m}$
Check options
- A: $80\,$ m ❌
- B: $200\,$ m ❌
- C: $120\,$ m ❌
- D: $320\,$ m ✅

Therefore, the correct answer is Option D.