Question
How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Answer: Option B
$$\eqalign{
& {\text{Speed}}\,{\text{of}}\,{\text{the}}\,{\text{train}}\,{\text{relative}}\,{\text{to}}\,{\text{man}} \cr
& = \left( {63 - 3} \right)\,{\text{km/hr}} \cr
& = 60\,{\text{km/hr}} \cr
& = \left( {60 \times \frac{5}{{18}}} \right)\,{\text{m/sec}} \cr
& = \frac{50}{3}\, \text{m/sec} \cr
& \therefore {\text{Time}}\,{\text{taken}}\,{\text{to}}\,{\text{pass}}\,{\text{the}}\,{\text{man}} \cr
& = \left( {500 \times \frac{3}{{50}}} \right)\,\sec \cr
& = 30\,\sec \cr} $$
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$$\eqalign{
& {\text{Speed}}\,{\text{of}}\,{\text{the}}\,{\text{train}}\,{\text{relative}}\,{\text{to}}\,{\text{man}} \cr
& = \left( {63 - 3} \right)\,{\text{km/hr}} \cr
& = 60\,{\text{km/hr}} \cr
& = \left( {60 \times \frac{5}{{18}}} \right)\,{\text{m/sec}} \cr
& = \frac{50}{3}\, \text{m/sec} \cr
& \therefore {\text{Time}}\,{\text{taken}}\,{\text{to}}\,{\text{pass}}\,{\text{the}}\,{\text{man}} \cr
& = \left( {500 \times \frac{3}{{50}}} \right)\,\sec \cr
& = 30\,\sec \cr} $$
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