A train crossed a 110 m long platform in 13.5 seconds and a 205 m long platform in 18.25 seconds. What was the speed of the train?

Correct option is D

Given:
- Length of platform 1 (P1) = 110 m
- Time to cross platform 1 (T1) = 13.5 seconds
- Length of platform 2 (P2) = 205 m
- Time to cross platform 2 (T2) = 18.25 seconds

Formula Used:
Speed of train = $$\frac{\text{Length of train} + \text{Length of platform}}{\text{Time}}$$​​

Solution:
Let length of train be L meters and speed be v m/s.

From platform 1:
​$$v = \frac{(L + 110) }{ 13.5}...(1)$$​​
From platform 2:
​$$v = \frac{(L + 205) }{18.25}...(2)$$​​
Equate (1) and (2):
​$$\frac{L + 110}{13.5} = \frac{L + 205}{18.25} \\\ \\\Rightarrow 18.25(L + 110) = 13.5(L + 205) \\\ \\\Rightarrow 18.25L + 2007.5 = 13.5L + 2767.5 \\\ \\\Rightarrow 18.25L - 13.5L = 2767.5 - 2007.5 \\\ \\\Rightarrow 4.75L = 760$$​​
=> L = 160 m
Now, find speed v:
​$$v =\frac{ (160 + 110) }{13.5 }= \frac{270 }{ 13.5 }= 20 m/s$$​​
Convert speed to km/hr:
Speed = $$20 × \frac{18 }{5}$$​ = 72 km/hr
Hence, the speed of the train is 72 km/hr.