Question
Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:
Answer: Option D
$$\eqalign{
& {\text{Relative}}\,{\text{speed}} = \left( {60 + 40} \right)\,{\text{km/hr}} \cr
& = {100 \times \frac{5}{{18}}} \,{\text{m/sec}} \cr
& = {\frac{{250}}{9}} \,{\text{m/sec}}. \cr
& {\text{Distance}}\,{\text{covered}}\,{\text{in}}\,{\text{crossing}}\,{\text{each}}\,{\text{other}} \cr
& = \left( {140 + 160} \right)m = 300\,m \cr
& {\text{Required}}\,{\text{time}} \cr
& = {300 \times \frac{9}{{250}}} \,{\text{sec}} \cr
& = \frac{{54}}{5}\,{\text{sec}} \cr
& = 10.8\,{\text{sec}} \cr} $$
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$$\eqalign{
& {\text{Relative}}\,{\text{speed}} = \left( {60 + 40} \right)\,{\text{km/hr}} \cr
& = {100 \times \frac{5}{{18}}} \,{\text{m/sec}} \cr
& = {\frac{{250}}{9}} \,{\text{m/sec}}. \cr
& {\text{Distance}}\,{\text{covered}}\,{\text{in}}\,{\text{crossing}}\,{\text{each}}\,{\text{other}} \cr
& = \left( {140 + 160} \right)m = 300\,m \cr
& {\text{Required}}\,{\text{time}} \cr
& = {300 \times \frac{9}{{250}}} \,{\text{sec}} \cr
& = \frac{{54}}{5}\,{\text{sec}} \cr
& = 10.8\,{\text{sec}} \cr} $$
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