Two trains, A and B, start simultaneously from stations Delhi and Mumbai respectively towards each other on parallel tracks. After meeting, train A takes 16 hours to reach Mumbai, and train B takes 9 hours to reach Delhi. If train A's speed is 60 km/h, what is the length of train B (in meters), given that it crosses a pole in 18 seconds?
400
Using the property of trains meeting: if after meeting, train A takes \(t_A\) hours and train B takes \(t_B\) hours to reach their respective destinations, then \(\frac{v_A}{v_B} = \sqrt{\frac{t_B}{t_A}}\).
Here \(t_A = 16\) h, \(t_B = 9\) h, so \(\frac{v_A}{v_B} = \sqrt{\frac{9}{16}} = \frac{3}{4}\).
Given \(v_A = 60\) km/h: \(\frac{60}{v_B} = \frac{3}{4}\), so \(v_B = 80\) km/h.
Convert train B's speed to m/s: \(80 \times \frac{1000}{3600} = \frac{200}{9}\) m/s.
Train B crosses a pole in 18 seconds, so its length \(= \frac{200}{9} \times 18 = 400\) m.
Hence, the length of train B is 400 metres.
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Important Questions from Problem on Trains
Eight railway stations A, B, C, D, E, F, G and H are connected either by two-way passages or one-way passages. One-way passages are from C to A, E to G, B to F, D to H, G to C, E to C and H to G. Two-way passages are between A and E, G and B, F and D, and E and D.
If the route between G and C is closed, which one of the following stations need not be passed through while travelling from H to C?
A daily train is to be introduced between station A and station B starting from each end at 6 AM and the journey is to be completed in 42 hours. What is the number of trains needed in order to maintain the Shuttle Service?
A train with a uniform speed passes a 122 meters long platform in 17 seconds and a 210 meters long bridge in 25 seconds. The speed of the train is:
How long does a train 153 meters long running at the rate of 90 kmph take to cross a bridge 622 meters in length?
A train passes a 360 metre long platform in 40 seconds and a man standing on the platform in 16 seconds. The speed of the train is:
