Question

Two trains cross each other in 14 seconds when running in opposite directions along parallel tracks. The faster train is 160 m long and crosses a lamp post in 12 seconds. If the speed of the other train is 6km/hr less than the faster one, its length, in m, is

• A. 184
• B. 180
• C. 190
• D. 192

Answer 1

The Correct Option is C

Let's solve the problem step by step. 

Step 1: Find the speed of the faster train. 

Given, the faster train crosses a lamp post in 12 seconds, and it is 160 m long. So, the speed of the faster train (V_f) is: 

\( Vf = \frac{Distance}{Time}\) = \(\frac{160m}{12s} = 13.33 \text{ m/s} \).

Step 2: Calculate the speed of the slower train. 

The speed of the slower train (Vs) is given to be 6 km/hr less than the faster train. 

First, convert the speed of the faster train to km/hr: 

\(V_f = 13.33 m/s = 13.33 \times \frac{3600}{1000} = 48 \text{ km/hr}\)

Now, subtracting 6 km/hr from 48 km/hr: 

\(V_s = 48 - 6 = 42 \text{ km/hr} = 11.67 \text{ m/s}\)

Step 3: Calculate the length of the slower train. When the two trains cross each other in opposite directions, their relative speed is the sum of their speeds:

\(V_{relative} = Vf + Vs = 13.33 + 11.67 = 25 \text{ m/s}\)

Now, given that they cross each other in 14 seconds, the combined length of both trains is: 

\(Distance_{combined} = V_{relative} \times Time = 25 \times 14 = 350m\)

Subtracting the length of the faster train from this combined length gives the length of the slower train: 

\(Length_{slower} = 350 - 160 = 190m\)

So, the correct answer is option (c): 190.

Answer 2

It takes 12 seconds for the 160-meter-long faster train to pass a lamppost.

The speed of the faster train = \(\frac{160}{12}=\frac{40}{3}\)m/s
The speed of the slower train = \(\frac{40}{3} - \left(6 \times \frac{5}{18}\right) = \frac{35}{3}\) m/s.

Given that, when traveling in opposite directions along parallel lines, the two trains will cross each other in 14 seconds.
Total speed (as the trains approach one another) =\(\frac{40}{3}+\frac{35}{3}=25\) m/s.

\(\text{Relative speed} = \frac{\text{Total length of two trains}}{\text{Time taken to cross each other}}\)

If the slower train has a length of x meters, then \(\frac{160 + x }{ 25} =14\)
\(⇒\)Length of the second train = 190m.