Question

Two trains of equal length take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train is 120 meters. In what time (in seconds) will they cross each other in opposite directions?
A. 16
b. 15
C. 12
D. 10

Answer 1

Hint:In this question, first of all find the relative speeds of the two trains by the given data. When two bodies move in the opposite direction then the relative speed is calculated as their sum. So, find the relative speed of the two trains when they cross each other in the opposite direction and hence calculate their time period. So, use this concept to reach the solution of the given question.

Complete step-by-step answer:
Given length of the first train = 120 m
Time taken by the first train to cross the telegraph post = 10 sec
And length of the second train = 120 m
Time taken by the second train to cross the telegraph post = 15 sec
We know that \[{\text{Speed }} = {\text{ }}\dfrac{{{\text{Distance}}}}{{{\text{Time period}}}}\]
Now consider the relative speeds of the two trains.
Relative speed of first train \[{v_1} = \dfrac{{120}}{{10}} = 12{\text{ m/sec}}\]
Relative speed of second train \[{v_2} = \dfrac{{120}}{{15}} = 8{\text{ m/sec}}\]
We know that when two bodies move in the opposite direction then the relative speed is calculated as their sum.
So, the relative speed of the trains when they cross each other in opposite directions is given by
\[
  v = {v_1} + {v_2} \\
  v = 12 + 8 \\
  \therefore v = 20{\text{ m/sec}} \\
\]
The total distance covered by the trains to cross each other in opposite directions is equal to the sum of their lengths which is given by \[d = 120 + 120 = 240{\text{ m}}\].
We know that \[{\text{time taken }} = {\text{ }}\dfrac{{{\text{Distance}}}}{{{\text{Speed}}}}\]
Therefore, require time \[ = \dfrac{{240}}{{20}} = 12{\text{ sec}}\]
Hence, the time taken (in seconds) by the trains to cross each other in opposite directions is 12 sec.
Thus, the correct option is C.12
Note: Relative speed is defined as the speed of a moving object with respect to another. In the given problem, if the two trains cross each other in the same direction then their relative speed is given by the difference of their relative speeds of both the trains.