Train 1 travelling at a speed of 80 km/hr leaves station A at 6:00 a.m., and train 2 travelling at 105 km/hr starts from station A at 8:30 a.m. in the same direction on a parallel track. At what distance (in km) from station A will train 2 meet train 1?

Correct option is B

Given:

Speed of Train 1 = 80 km/hr

Speed of Train 2 = 105 km/hr

Train 1 leaves Station A at 6:00 a.m.

Train 2 leaves Station A at 8:30 a.m., 2.5 hours later.

Solution:

Time gap between the two trains:
Train 2 starts 2.5 hours later than Train 1.
In this 2.5 hours, Train 1 will cover:

Distance covered by Train 1 in 2.5 hours = Speed × Time = 80 km/hr × 2.5 hrs = 200 km

Since both trains are moving in the same direction, the relative speed is the difference in their speeds:

Relative speed = 105 km/hr − 80 km/hr = 25 km/hr

Time taken for Train 2 to catch up with Train 1:

Time =$$\frac{\text{Distance}}{\text{Relative speed}} = \frac{200}{25} = 8 \, \text{hours}$$​​

Distance at which they meet:
Train 2 will meet Train 1 after 8 hours of travel from 8:30 a.m. (when Train 2 starts). The distance traveled by Train 2 in 8 hours is:

Distance traveled by Train 2= $$105 \, \text{km/hr} \times 8 \, \text{hrs} = 840 \, \text{km}$$​

Train 2 will meet Train 1 at a distance of 840 km from Station A.