Shortcut Trick
When time is constant, Distance ∝ Speed.
Difference in Speed = 95 − 80 = 15 km/h.
Total Speed = 95 + 80 = 175 km/h.
Total Distance = (Total Speed ÷ Difference in Speed) × Difference in Distance
Total Distance = (175 ÷ 15) × 180 = 175 × 12 = 2100 km.
∴ The correct answer is 2100 km.
Alternate Method
Given:
Speed of first train = 80 km/h
Speed of second train = 95 km/h
Difference in distance travelled at meeting time = 180 km
Formula Used:
Distance = Speed × Time
Calculations:
⇒ Let the time taken for both trains to meet be t hours.
⇒ Distance covered by first train = 80 × t
⇒ Distance covered by second train = 95 × t
⇒ The difference in distance covered = 95t − 80t = 15t
⇒ 15t = 180
⇒ t = 180 ÷ 15 = 12 hours
⇒ Total distance between Bangalore and Chennai = 80t + 95t = 175t
⇒ Total distance = 175 × 12
⇒ Total distance = 2100 km
∴ The correct answer is 2100 km.
Additional Information
Relative Speed (Opposite Directions)
When two bodies move towards each other, their relative speed is the sum of their individual speeds (S1 + S2).
Relative Speed (Same Direction)
When two bodies move in the same direction, their relative speed is the difference of their individual speeds (|S1 − S2|).
Constant Time Property
If two objects travel for the exact same amount of time, the ratio of distances they cover is equal to the ratio of their respective speeds (D1 ÷ D2 = S1 ÷ S2).