Two trains 230 m and 270 m long are running in opposite directions at speeds of 42 km/h and 48 km/h, respectively. They cross each other in:

The correct answer is 20 seconds.

To find the time taken for the two trains to cross each other completely, we calculate the total distance covered and the relative speed of the two trains.

Step 1: Calculate the total distance
When two trains cross each other, the total distance that needs to be covered is equal to the sum of the lengths of both trains.

Length of the first train = 230 m
Length of the second train = 270 m

$\text{Total Distance}=230\text{m}+270\text{m}=500\text{m}$

Step 2: Calculate the relative speed
Since the two trains are running in opposite directions, their relative speed is the sum of their individual speeds.

Speed of the first train = 42 km/h
Speed of the second train = 48 km/h

$\text{Relative Speed}=42\text{km/h}+48\text{km/h}=90\text{km/h}$

Step 3: Convert the relative speed to meters per second (m/s)
To convert speed from km/h to m/s, multiply by $\frac{5}{18}$:

$\text{Relative Speed in m/s}=90\times \frac{5}{18}\text{m/s}=25\text{m/s}$

Step 4: Calculate the time taken to cross
Using the speed, distance, and time formula:

$\text{Time}=\frac{\text{Total Distance}}{\text{Relative Speed}}$

$\text{Time}=\frac{500\text{m}}{25\text{m/s}}=20\text{seconds}$

Hence, the two trains cross each other in 20 seconds.