Train A passes a lamp post in 9 seconds and 700 meter long platform in 30 seconds. How much time will the same train take to cross a platform which is 800 meters long?

Let the length of the train is x m. and its speed is v. m/s.

Distance = Speed × time [S = V × T]
x = v × 9 .........(i).
(x+700) = v × 30 ........(ii).

Dividing the eqn. (i) by (ii).

x/(x+700)= 3/10.
⇒ 10x=3x + 2100.
⇒ 7x=2100.
⇒ x= 2100/7.
⇒ x= 300. m.

putting x = 300 in eqn. (1).
300 = v × 9
⇒ v = 300/9
⇒ v = 100/3 m/s.

Let the train crosses a 800 m. long platform in t seconds.
(x + 800) = v × t .........(iii) [ S = V × T]
⇒ (300 + 800) = (100/3) × t. [putting x= 300. and v= 100/3.]
⇒ t = (1100×3)/100
⇒ t = 33 seconds.