An express tram measuring 200 meters in length takes 10 seconds to clear a stationary marker post. When moving in the opposite direction against another tram of equal length, it completely passes it in 8 seconds. What is the speed of the second tram?

The correct option is 108 km/h.

To find the speed of the second tram, we can break down the solution into logical step-by-step calculations.

Step 1: Calculate the speed of the express tram
When a tram passes a stationary marker post, the distance covered is equal to the length of the tram itself.

Length of the express tram ($L_1$) = 200 meters
Time taken ($t_1$) = 10 seconds

The speed of the express tram ($v_1$) is given by the formula:

$v_1=\frac{L_1}{t_1}$

$v_1=\frac{200}{10}=20\text{m/s}$

Step 2: Calculate the relative speed of the two trams
When two trams moving in opposite directions completely pass each other, the total distance covered is equal to the sum of their lengths.

Length of the second tram ($L_2$) = 200 meters (since both trams are of equal length)

Total distance covered ($D$):

$D=L_1+L_2=200+200=400\text{meters}$

Time taken to completely pass each other ($t_2$) = 8 seconds

The relative speed ($v_{\text{rel}}$) of the two trams is:

$v_{\text{rel}}=\frac{D}{t_2}$

$v_{\text{rel}}=\frac{400}{8}=50\text{m/s}$

Step 3: Determine the speed of the second tram in m/s
Because the two trams are moving in opposite directions, their relative speed is the sum of their individual speeds:

$v_{\text{rel}}=v_1+v_2$

Substituting the known values:

$50=20+v_2$

$v_2=50-20=30\text{m/s}$

Step 4: Convert the speed into km/h
To convert speed from meters per second (m/s) to kilometers per hour (km/h), multiply by $\frac{18}{5}$:

$v_2=30\times \frac{18}{5}$

$v_2=6\times 18=108\text{km/h}$

Therefore, the speed of the second tram is 108 km/h.