1.

Two men are running in the same direction with a speed of 6 km/hr and \(7\frac12\) km/hr. A train running in the same direction crosses them in 5 sec and \(5\frac12\) sec respectively. The length and the speed of the train are (a) 22.92 m (approx) and 22 km/hr (b) 22 m (approx) and 22.5 km/hr (c) 22.90 m (approx) and 20.5 km/hr (d) 22.92 m (approx) and 22.5 km/hr

Answer»

(d) 22.92 m (approx) abd 22.5 km/hr

Let the length of the train be l m and its speed be x km/hr. 

Then, relative speed of train w.r.t.1st man 

= (x – 6) km/hr = (x - 6) x \(\frac{5}{18}\) m/s

Relative speed of train w.r.t. 2nd man 

= (x – 7.5) km/hr = (x - 7.5) x \(\frac{5}{18}\) m/s

Length of the train = Distance travelled in both the cases

⇒  (x - 6) x \(\frac{5}{18}\) x 5 = (x - 7.5) x \(\frac{5}{18}\) x 5.5

⇒  (x - 6) x 5 = (x - 7.5) x 5.5

⇒ 5x – 30 = 5.5x – 41.25 ⇒ 0.5x = 11.25

⇒ \(x\) = \(\frac{11.25}{0.5}\) = 22.5 km/hr

∴ Length of the train = \(\bigg((22.5-6)\times\frac{5}{18}\times5\bigg)\) m

= 22.92 m (approx)


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