A train leaves a station A at 7 am and reaches another station B at 11 am. Another train leaves B at 8 am and reaches A at 11.30 am. The two trains cross one another at

Solution (By Examveda Team)

Here's a breakdown of how to solve this train problem, explained in a simple way:

First, let's figure out how long each train takes to complete its journey:
Train 1 (from A to B): It travels from 7:00 am to 11:00 am, which is a total of 4 hours.
Train 2 (from B to A): It travels from 8:00 am to 11:30 am, which is a total of 3.5 hours (or 3 and a half hours).

Now, imagine the distance between A and B as 'D'. We can calculate the speed of each train:
Speed of Train 1: D / 4 (Distance divided by time)
Speed of Train 2: D / 3.5 (Distance divided by time)

Let's see what happens in the first hour after Train 1 starts (from 7 am to 8 am). In this hour, only Train 1 is moving.
Now, consider the time after 8 am. Let 't' be the time (in hours) after 8 am when the trains meet.
In time 't', Train 1 covers a distance of (D/4) * t
In time 't', Train 2 covers a distance of (D/3.5) * t

When they meet, the combined distance covered by both trains will be equal to the distance between A and B (which is D). The important thing to note is that Train 1 has already been traveling for an hour (from 7am to 8am) before Train 2 departs.
Therefore the equation should be: (Distance covered by train 1 in 1 hour) + (Distance covered by train 1 in 't' hours) + (Distance covered by train 2 in 't' hours) = Total Distance
(D/4 * 1) + (D/4 * t) + (D/3.5 * t) = D

Now, simplify the equation by dividing the entire equation by D
(1/4) + (t/4) + (t/3.5) = 1
Solve for 't':
(t/4) + (t/3.5) = 1 - (1/4)
(t/4) + (t/3.5) = 3/4
To solve easily, convert 3.5 to 7/2
(t/4) + (2t/7) = 3/4
Find a common denominator to combine the t terms
(7t/28) + (8t/28) = 3/4
(15t/28) = 3/4
Multiply both sides by 28
15t = (3/4) * 28
15t = 21
t = 21/15 = 7/5 hours

Convert 7/5 hours into hours and minutes:
t = 1 hour and (2/5) of an hour
(2/5) of an hour = (2/5) * 60 minutes = 24 minutes
So, t = 1 hour and 24 minutes.

Since 't' is the time after 8:00 am, add 1 hour and 24 minutes to 8:00 am:
8:00 am + 1 hour 24 minutes = 9:24 am

Therefore, the two trains cross one another at 9:24 am.
The answer is (D).