Question
A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:
Answer: Option B
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2 kmph = \(\left(2\times\frac{5}{18}\right)m/sec= \frac{5}{9}m/sec\)
4 kmph =\(\left(4\times\frac{5}{18}\right)m/sec = \frac{10}{9}m/sec\)
Let the length of the train be x metres and its speed by y m/sec.
Then, \(\left[\frac{x}{y-\frac{5}{9}}\right]=9 and
\left[\frac{x}{y-\frac{10}{9}}\right] = 10\)
Therefore 9y - 5 = x and 10(9y - 10) = 9x
9y - x = 5 and 90y - 9x = 100.
On solving, we get: x = 50.
Therefore Length of the train is 50 m.
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