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Train A takes 45 seconds to cross a tunnel while train B of same length takes 75 seconds to cross the same tunnel. The ratio of length of train and length of tunnel is 2 : 3. How long is the tunnel if the difference in the speeds of train is 20 m/s?

Train A takes 45 seconds to cross a tunnel while train B of same length takes 75 seconds to cross the same tunnel. The ratio of length of train and length of tunnel is 2 : 3. How long is the tunnel if the difference in the speeds of train is 20 m/s? Correct Answer 1350 m

Let the speed of train A be s m/s and that of train B be s - 20 m/s.

Distance covered by train A = distance covered by train B

∴ s × 45 = (s - 20) × 75

⇒ s = 50m/s

Distance travelled by train A = 50 × 45 = 2250 m

Let x be any number such that length of the trains is 2x and the length of tunnel is 3x.

Distance covered by train A = length of the train + length of the tunnel

∴ 2x + 3x = 2250

⇒ 5x = 2250

⇒ x = 450

∴ length of the tunnel, 3x = 1350 m

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