Two stations T1 and T2 300 km apart. A car starts from station T1 at 8 am and moves towards station T2 at a speed of 45km/hr. and at 10 am another car starts from station T2 towards T1 at a speed of 60km/hr. Then the cars will meet at:

The correct answer is Option 2: 12:00 p.m.

Step-by-Step Explanation:

1. Understand the given data:
Total distance between station T₁ and station T₂ = 300 km.
Speed of the first car (starting from T₁ at 8:00 a.m.) = 45 km/h.
Speed of the second car (starting from T₂ at 10:00 a.m.) = 60 km/h.

2. Calculate the distance covered by the first car before the second car starts:
Time elapsed from 8:00 a.m. to 10:00 a.m. = 2 hours.
Distance covered by the first car in 2 hours = speed × time
$\text{Distance covered}=45\times 2=90\text{km}$

3. Calculate the remaining distance between the two cars at 10:00 a.m.:
$\text{Remaining distance}=300-90=210\text{km}$

4. Calculate the relative speed when both cars are moving towards each other:
Since both cars travel in opposite directions towards each other, their speeds add up.
$\text{Relative speed}=45+60=105\text{km/h}$

5. Calculate the time taken to cover the remaining distance:
$\text{Time taken}=\frac{210}{105}=2\text{hours}$

6. Determine the exact meeting time:
Adding 2 hours to 10:00 a.m.:
10:00 a.m. + 2 hours = 12:00 p.m.

Therefore, the two cars will meet at 12:00 p.m.