# Ram is sitting in a train A going from Delhi to Chandigarh which starts at 9 am in the morning running at 70 km/hr while Shyam is sitting in a train B

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Ram is sitting in a train A going from Delhi to Chandigarh which starts at 9 am in the morning running at 70 km/hr while Shyam is sitting in a train B coming from Chandigarh to Delhi will start at 10:30 am and will run at the speed of 80 km/hr. Find the time at which Ram and Shyam will meet if the distance between Delhi and Chandigarh is 480 km.
1. 12:30 pm
2. 1:00 pm
3. 1:30 pm
4. 12:10 pm
5. 12:45 pm

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Correct Answer - Option 2 : 1:00 pm

Given:

Speed of train A = 70 km/hr

Speed of train B = 80 km/hr

Train A starts at 9 am

Train B starts at 10:30 am

Distance between Delhi and Chandigarh = 480 km

Concept used:

Relative speed is defined as the speed of a moving object with respect to another. When two objects are moving in the same direction, relative speed is calculated as their difference. When the two objects are moving in opposite directions, relative speed is computed by adding the two speeds.

Formula used:

Distance = Time × Speed

Calculation:

Train A starts at 9 am

Train B starts at 10:30 am

Distance covered by Train A between 9 am and 10:30 am

Speed of Train A = 70 km/hr

Time between 10:30 am and 9 am = 1.5 hours

Distance covered by A in 1.5 hours = 70 × 1.5

⇒ Distance covered by A till 10:30 am = 105 km

Now, Total distance = 480 km

Distance already covered by A = 105 km

Now, Distance to be covered = (480 – 105) km

⇒ Distance to be covered = 375 km

Now, both trains will cover this distance and both trains are running in opposite direction

So, when the two objects are moving in opposite directions, relative speed is computed by adding the two speeds

⇒ Relative speed = (70 + 80) = 150 km/hr

Distance to be covered = 375 km

Time taken to meet = 375/150

⇒ Time taken to meet = 2.5 hours

⇒ The time at which both trains will meet = (10:30 + 2:30)

⇒ Both trains will meet at = 1 pm