Two trains of equal length are running on parallel lines in the same direction at speeds of 112 km/h and 46 km/h. The faster train passes the slower train in 12 seconds. The length of each train is:

Correct option is A

Given:

Speed of the faster train (S₁) = 112 km/h

Speed of the slower train (S₂) = 46 km/h

Time taken to pass (t) = 12 seconds

Length of both trains are equal.

Formula Used:

When two objects move in the same direction, their relative speed is the difference between their speeds.

Relative Speed = S₁ - S₂

Distance = Relative Speed × Time

The total distance covered for one train to completely pass another is the sum of their lengths.

Total Distance = Length of Train 1 + Length of Train 2

To convert speed from km/h to m/s, multiply by $$\frac 5{18}$$.​

Solution:

Relative Speed = 112 - 46 = 66 km/h

Relative Speed (m/s) = 6$$6 \times \frac{5}{18} = \frac{330}{18} = \frac{55}{3} \, \text{m/s}$$​

Total Distance $$= \text{Relative Speed} \times \text{Time}$$​

Total Distance =$$\frac{55}{3} \times 12 = 220 \, \text{m}$$​
Since both trains are of equal length, the length of each train is half the total distance.

Length of each train = $$\frac{220}{2} = 110 \, \text{m}$$​

Therefore, the length of each train is 110 m.