a) 180 metres
b) 200 metres
c) 210 metres
d) 240 metres
Answer: c
Explanation: 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, train need to travel (2X + Y) m to cross the platform.
$$\eqalign{
& {\text{Speed}} = \frac{{{\text{Distance}}}}{{{\text{Time}}}} \cr
& 15 = \frac{{{\text{2X}} + {\text{Y}}}}{{46}} \cr
& {\text{2X}} + {\text{Y}} = 690\,.\,.\,.\,.\,.\,.\,.\,.\left( 2 \right) \cr} $$
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
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