A train travelling at 60 km/hr crosses another train travelling in the opposite direction at 84 km/hr in 30 seconds. What is the combined length (in m) of both the trains?

The correct option is 1200.

Step-by-step Explanation:

Step 1: Understand the given values

Speed of the first train, $s_1=60\text{km/hr}$

Speed of the second train, $s_2=84\text{km/hr}$

Time taken to cross each other, $t=30\text{seconds}$

Step 2: Calculate the relative speed

Since the two trains are travelling in opposite directions, their relative speed is the sum of their individual speeds:

$\text{Relative Speed}=s_1+s_2$

$\text{Relative Speed}=60+84=144\text{km/hr}$

Step 3: Convert speed from km/hr to m/s

To convert speed from kilometers per hour (km/hr) to meters per second (m/s), multiply by $\frac{5}{18}$:

$\text{Speed in m/s}=144\times \frac{5}{18}$

$\text{Speed in m/s}=8\times 5=40\text{m/s}$

Step 4: Calculate the combined length of both trains

The total distance covered by the trains when passing each other is equal to the combined length of both trains.

$\text{Distance}=\text{Relative Speed}\times \text{Time}$

$\text{Combined Length}=40\text{m/s}\times 30\text{s}$

$\text{Combined Length}=1200\text{meters}$

Therefore, the combined length of both the trains is 1200 m.