Train ‘A’ can cross a pole and 200 meters long platform in 16 seconds & 24 seconds respectively. Find time taken by train ‘A’ to cross another train’ B’, which length is 480 meters and running at the speed of 108 km/hr in opposite direction.

Correct Answer: 16 seconds

Step-by-Step Explanation:

Step 1: Find the speed of Train A

Let the length of Train A be _L meters and its speed be _v m/s.

When Train A crosses a pole, it covers its own length in 16 seconds:

$v=\frac{L}{16}$

When Train A crosses a 200 meters long platform, it covers a total distance equal to its own length plus the platform length in 24 seconds:

$v=\frac{L+200}{24}$

Equating the two expressions for speed _v:

$\frac{L}{16}=\frac{L+200}{24}$

Cross-multiplying or simplifying the denominators by dividing both 16 and 24 by 8:

$\frac{L}{2}=\frac{L+200}{3}$

$3L=2L+400$

$L=400\text{meters}$

Now, calculate the speed of Train A (_v):

$v=\frac{400}{16}=25\text{m/s}$

Step 2: Find the speed of Train B in m/s

The speed of Train B is given as 108 km/hr. To convert it into m/s, multiply by $\frac{5}{18}$:

$\text{Speed of Train B}=108\times \frac{5}{18}=30\text{m/s}$

Step 3: Calculate the relative speed and total distance to cross Train B

Since Train A and Train B are moving in opposite directions, their relative speed is the sum of their speeds:

$\text{Relative Speed}=25+30=55\text{m/s}$

The total distance to be covered while crossing Train B is the sum of the lengths of both trains:

$\text{Total Distance}=\text{Length of Train A}+\text{Length of Train B}$

$\text{Total Distance}=400+480=880\text{meters}$

Step 4: Find the time taken

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

$\text{Time taken}=\frac{880}{55}=16\text{seconds}$

Thus, the time taken by Train A to cross Train B is 16 seconds.