Question
A man standing on a platform finds that a train takes 3 seconds to pass him and another train of the same length moving in the opposite direction takes 4 seconds. The time taken by the trains to pass each other will be :
Answer: Option B
Let the length of each train be x meters
Then, speed of first train = $$\frac{{\text{x}}}{3}$$ m/sec
Speed of second train = $$\frac{{\text{x}}}{4}$$ m/sec
∴ Required time
$$\eqalign{
& = \left[ {\frac{{{\text{x}} + {\text{x}}}}{{\left( {\frac{{\text{x}}}{3} + \frac{{\text{x}}}{4}} \right)}}} \right]{\text{sec}} \cr
& = \left[ {\frac{{2{\text{x}}}}{{\left( {\frac{{7{\text{x}}}}{{12}}} \right)}}} \right]{\text{sec}} \cr
& = \left( {2 \times \frac{{12}}{7}} \right){\text{sec}} \cr
& = \frac{{24}}{7}{\text{sec}} \cr
& = 3\frac{3}{7}{\text{sec}} \cr} $$
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Let the length of each train be x meters
Then, speed of first train = $$\frac{{\text{x}}}{3}$$ m/sec
Speed of second train = $$\frac{{\text{x}}}{4}$$ m/sec
∴ Required time
$$\eqalign{
& = \left[ {\frac{{{\text{x}} + {\text{x}}}}{{\left( {\frac{{\text{x}}}{3} + \frac{{\text{x}}}{4}} \right)}}} \right]{\text{sec}} \cr
& = \left[ {\frac{{2{\text{x}}}}{{\left( {\frac{{7{\text{x}}}}{{12}}} \right)}}} \right]{\text{sec}} \cr
& = \left( {2 \times \frac{{12}}{7}} \right){\text{sec}} \cr
& = \frac{{24}}{7}{\text{sec}} \cr
& = 3\frac{3}{7}{\text{sec}} \cr} $$
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