Question
A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Answer: Option B
$$\eqalign{
& {\text{Speed}} = {\frac{{300}}{{18}}} \,{\text{m/sec}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{50}}{3}\,{\text{m/sec}} \cr
& {\text{Let}}\,{\text{the}}\,{\text{length}}\,{\text{of}}\,{\text{the}}\,{\text{platform}}\,{\text{be}}\,x\,{\text{metres}}{\text{.}} \cr
& {\text{Then}}, {\frac{{x + 300}}{{39}}} = \frac{{50}}{3} \cr
& \Rightarrow 3\left( {x + 300} \right) = 1950 \cr
& \Rightarrow x = 350\,m. \cr} $$
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$$\eqalign{
& {\text{Speed}} = {\frac{{300}}{{18}}} \,{\text{m/sec}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{50}}{3}\,{\text{m/sec}} \cr
& {\text{Let}}\,{\text{the}}\,{\text{length}}\,{\text{of}}\,{\text{the}}\,{\text{platform}}\,{\text{be}}\,x\,{\text{metres}}{\text{.}} \cr
& {\text{Then}}, {\frac{{x + 300}}{{39}}} = \frac{{50}}{3} \cr
& \Rightarrow 3\left( {x + 300} \right) = 1950 \cr
& \Rightarrow x = 350\,m. \cr} $$
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