Question

A train is travelling with the speed of 72 km/hr and it takes 30 seconds to cross a platform. Another train which is 50 meter shorter crosses the same platform at the speed of 54 km/hr. Find the time taken by the second train to cross the platform.
1. 115/3 seconds
2. 111/3 seconds
3. 109/3 seconds
4. 110/3 seconds
5. 100/3 seconds

Answer 1

Correct Answer - Option 4 : 110/3 seconds

Given:

Speed of larger train = 72 km/hr

Speed of shorter train = 54 km/hr

Length of shorter train = Length of larger train – 50

Time to cross platform by larger train = 30 seconds

Concept used:

Distance = Speed × Time

And, Length of train + Length of platform = Total distance

Speed in m/s = 5/18 × Speed in km/hr

Calculation:

Let length of larger train be L and length of platform be P

∴ Length of shorter train = L – 50

Time taken by shorter train = T

Now, Total distance covered by larger train = L + P

Speed of larger train = 72 km/hr

Speed of larger train in m/s = 72 × 5/18

⇒ Speed of larger train = 20 m/s

Time taken to cover the distance = 30 seconds

So, Distance = Speed × Time

⇒ L + P = 30 × 20

⇒ L + P = 600      ----(i)

Now, length of shorter train = L – 50

Total distance covered by shorter train = L – 50 + P

Speed of shorter train = 54 km/hr

Speed of shorter train in m/s = 54 × 5/18

⇒ Speed of shorter train in m/s = 15 m/s

Time taken by shorter train = T

So, Distance = Speed × Time

⇒ L + P – 50 = 15 × T      ----(ii)

Now, putting value of equation (i) and (ii)

⇒ 600 – 50 = 15T

⇒ 15T = 550

⇒ T = 550/15

⇒ T = 110/3 seconds

∴ Time taken by shorter train to cover the platform = 110/3 seconds