A train running at a speed of 54 km/hr crosses a platform in 30 seconds. The platform is renovated and its length is doubled. Now, the same train running at same speed crosses the platform in 46 seconds. Find the length of the train.

Solution(By Examveda Team)

Let length of the Platform is X m and Train is Y m.
Speed of the train = 54 kmph = $$\frac{{54 \times 5}}{{18}}$$ = 15 m/sec.
To cross the platform, train needs to travel (X + Y) m in 30 sec.
$$\eqalign{ & {\text{Speed}} = \frac{{{\text{Distance}}}}{{{\text{Time}}}} \cr & 15 = \frac{{{\text{X}} + {\text{Y}}}}{{30}} \cr & {\text{X}} + {\text{Y}} = 450\,.\,.\,.\,.\,.\,.\,.\,.\,.\,.\,.\left( 1 \right) \cr} $$
Now Platform is renovated and its length is doubled. So, Now, train need to travel (2X + Y) m to cross the platform.
Thus,
$$\eqalign{ & {\text{Speed}} = \frac{{{\text{Distance}}}}{{{\text{Time}}}} \cr & 15 = \frac{{{\text{2X}} + {\text{Y}}}}{{46}} \cr & {\text{2X}} + {\text{Y}} = 690\,.\,.\,.\,.\,.\,.\,.\,.\,.\,.\,.\left( 2 \right) \cr} $$
Multiplying equation (1) by (2)
2X + 2Y = 900 ------------------ (3)
Now, equation (2) - (3)
2X + Y - 2X - 2Y = 690 - 900
- Y = - 210
Y = 210
Length of the train = 210 metres