Aptitude Discussion

Q. |
A train leaves station $X$ at 5am and reaches station $Y$ at 9 am. Another train leaves station $Y$ at 7 am and reaches station $X$ at 10:30 am. At what time do the two trains cross each other? |

✖ A. |
7:36 am |

✔ B. |
7:56 am |

✖ C. |
8:36 am |

✖ D. |
7:56 am |

**Solution:**

Option(**B**) is correct

Let the distance between $X$ and $Y$ is $d$ km

Then, speed of $A$ is \(\dfrac{d}{4}\) km/hr and that of $B$ is \(\dfrac{2d}{7}\) km/hr.

$X$ ------------------- $Y$ ($XY$ = $d$ km)

Relative speed = \(\dfrac{d}{4}+\dfrac{2d}{7}=\dfrac{15d}{28}\)km/hr

Now distance between these trains at 7 am \(=d-\dfrac{d}{2}=\dfrac{d}{2}\) km

Hence, time = \(\dfrac{d/2}{15d/28}=\dfrac{14}{15}\times 60=56\)

Hence both of them meet at **7:56 am**

**Kalyan**

*()
*

in this why we find out relative speed. i con't understand it