Question

Two trains are moving in opposite directions at speeds of 50 km/h and 110 km/h. The length of one train is 500 m. The time taken by them to cross each other is 12 seconds. The length (in m) of the other train, correct to 2 decimal places, is:

• A. 33.33
• B. 34.58
• C. 31.44
• D. 32.68

Answer 1

Answer:

A. 33.33

Step 1: Relative speed (opposite directions)

$50 + 110 = 160 \text{ km/h}$

Convert km/h to m/s:

$160 \times \frac{5}{18} = \frac{800}{18} = \frac{400}{9} \text{ m/s}$
$= 44.44\overline{4} \text{ m/s}$

Step 2: Total distance covered while crossing

Time = 12 seconds

$\text{Total length of both trains} = \text{Speed} \times \text{Time}$
$= \frac{400}{9} \times 12$
$= \frac{400 \times 12}{9}$
$= \frac{4800}{9}$
$= 533.33\overline{3} \text{ m}$
Step 3: Find length of other train

$\text{Other train length} = 533.33 - 500$
$= 33.33 \text{ m (approx)$

Final Answer: 33.33 m