Question

A train ‘X’ leaves station ‘A’ at \[3p.m.\]and reaches station ‘B’ at , while another train ‘Y’ leaves station ‘B’ at and reaches sta$4:30p.m.$tion ‘A’ at $4p.m.$. There two trains cross each other at:
A) $3.36p.m.$
B) $3.30p.m.$
C) $3.20p.m.$
D) $3.40p.m.$

Answer 1

Hint: First, let the distance between the stations and evaluate the speeds of each train. Speed is the ratio of distance to the time taken. After that assume the time after they meet and equate the distance travelled by each train to the total distance and evaluate the time.

Complete step-by-step answer:
We are given that a train ‘X’ leaves station ‘A’ at \[3p.m.\]and reaches station ‘B’ at $4:30p.m.$, while another train ‘Y’ leaves station ‘B’ at \[3p.m.\]and reaches station ‘B’ at $4p.m.$
Let the distance between the two stations A and B is $d$.
We know that speed is the ratio of distance to the time taken.
Time taken by train X is $1$ hour and $30$minutes or $1.5$hours therefore, the speed of the train X will be,
 $\dfrac{d}{{1.5}} = \dfrac{{2d}}{3}km/h$
Time taken by train Y is $1$ hour therefore, the speed of the train Y will be,
 $\dfrac{d}{1} = dkm/h$
Let the trains meet $x$hours after \[3p.m.\]
We know that distance is the product of the speed and the time.
The speed of the train X is \[\dfrac{{2d}}{3}km/h\]
Therefore, distance travelled by train X in $x$hours is \[x \times \dfrac{{2d}}{3}km\]
The speed of the train X is \[dkm/h\]
Therefore, distance travelled by train X in $x$hours is \[x \times dkm\]
We know that the total distance between the stations is $d$.
Write the expression for the total distance.
$x \times \dfrac{{2d}}{3} + x \times d = d$
Evaluate the value of $x$.
\[
  \dfrac{{2x}}{3} + x = 1 \\
  \dfrac{{5x}}{3} = 1 \\
  x = \dfrac{3}{5} \\
 \]
It means the trains meet $\dfrac{3}{5}$hours after \[3p.m.\]
Convert hours into minutes.
$
  1hour = 60\min \\
  \dfrac{3}{5}hour = \dfrac{3}{5} \times 60\min = 36\min \\
 $
Therefore, both the trains meet at $3.36p.m.$
Therefore, option (A) is correct.

Note: In these types of questions be careful about the unit of speed, distance and time.
You can solve this question by converting each time unit into minutes and evaluate the required time in minutes.