Question

Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speed is
a) 1:3
b) 3:2
c) 3:4
d) None of these

Answer 1

Hint: For solving this problem, let the speed of one train be x and the speed of another train be y in meters per second. By using the given statement, we equate time to obtain the speed ratio.
Complete step-by-step answer:
According to the problem statement, the time of crossing of a man standing on the platform is 27 seconds and 17 seconds. Let the speed of one train be x and the speed of other train be y in meter per second
As speed is defined as the ratio of distance and time. So, distance is the product of speed and time. This can be mathematically expressed as:
$\begin{align}
  & \text{speed = }\dfrac{\text{distance}}{\text{time}} \\
 & \text{distance = speed}\times \text{time} \\
\end{align}$
Therefore, distance travelled by first train = 27x m.
Distance travelled by second train = 17y m.
Also, the time of crossing over by two trains is 23 seconds. Now, time can be related as
$\text{time = }\dfrac{\text{distance}}{\text{speed}}$
The total distance travelled (27x + 17y) m.
The total speed is the relative speed and since both the trains are moving in opposite directions their speed is added. So, the final speed for crossover = x + y
Therefore, the time taken to cross over
\[\begin{align}
  & \dfrac{27x+17y}{x+y}=23 \\
 & 27x+17y=23x+23y \\
 & 27x-23x=23y-17y \\
 & 4x=6y \\
 & \dfrac{x}{y}=\dfrac{6}{4}=\dfrac{3}{2} \\
\end{align}\]
Hence, the obtained ratio is $\dfrac{3}{2}$.
Therefore, option (b) is correct.
Note: Students must be careful while calculating the relative speed of the train for crossover according to the given condition. Total distance must be calculated by multiplying the time with corresponding speed.