Two trains having lengths of 430 m and 120 m are running at speeds of 70 km/h and 100 km/h, respectively, in the same direction. The time taken (in minutes) by the faster train, coming from behind, to completely cross the other train is:

The correct option is 1.1.

To find the time taken by the faster train to completely cross the other train when running in the same direction, we can use the concept of relative speed and total distance.

Step 1: Calculate the total distance to cover
When one train crosses another train, the total distance to be covered is the sum of the lengths of both trains.
$\text{Total Distance}=L_1+L_2$
$\text{Total Distance}=430\text{m}+120\text{m}=550\text{m}$

Step 2: Calculate the relative speed
Since both trains are running in the same direction, the relative speed is the difference between their speeds.

Step 3: Convert the relative speed into meters per second (m/s)
To convert speed from km/h to m/s, we multiply by $\frac{5}{18}$:
$\text{Relative Speed}=30\times \frac{5}{18}\text{m/s}=\frac{25}{3}\text{m/s}$

Step 4: Calculate the time taken in seconds
Using the formula:
$\text{Time}=\frac{\text{Total Distance}}{\text{Relative Speed}}$
$\text{Time}=\frac{550}{25/3}=550\times \frac{3}{25}=22\times 3=66\text{seconds}$

Step 5: Convert the time into minutes
$\text{Time in minutes}=\frac{66}{60}=1.1\text{minutes}$

Therefore, the time taken by the faster train to completely cross the other train is 1.1 minutes.