1.

If a train takes 1.5 seconds to cross a telegraph post and 1.75 seconds to overtake a cyclist racing along a road parallel to the track at 10 m/s, then the length of the train is (a) 135 metres (b) 125 metres (c) 115 metres (d) 105 metres

Answer»

(d) 105 metres

Let the length of train be l metres and its speed be x m/s.

Then, \(\frac{l}{x} = 1.5 ⇒l=1.5x\)              .....(i)

and \(\frac{l}{(x-10)}=1.75 ⇒ l = 1.75(x-10)\)

⇒ l = 1.75x – 17.5                ...(ii)

From (i) and (ii), 

1.5x = 1.75x – 17.5 ⇒ 0.25x = 17.5

⇒ x = \(\frac{17.5}{0.25}\) = 70 m/s

∴ Length of the train = (1.5 × 70) metres = 105 metres.


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