Two trains 240 meters and 270 meters in length are running towards each other are parallel lines. at the ratio of 60 kmph and another at 48 kmph. How much time will they take to cross each other?t

Correct option is A

Given:

1. Length of the first train = 240 meters

2. Length of the second train = 270 meters

3. Speed of the first train = 60 kmph

4. Speed of the second train = 48 kmph

5. Trains are moving towards each other.

Formula Used:

1. Relative speed when objects move towards each other:

​$$\text{Relative Speed} = \text{Speed of Train 1} + \text{Speed of Train 2}$$​​

2. Time to cross each other:

​$$\text{Time} = \frac{\text{Sum of lengths of trains}}{\text{Relative Speed}}$$​​

Solution:

1. Convert speeds from kmph to m/s:

To convert kmph to m/s, multiply by $$\frac{5}{18}$$​ :

​$$\text{Speed of Train 1} = 60 \times \frac{5}{18} = 16.67 m/s$$​​

​$$\text{Speed of Train 2} = 48 \times \frac{5}{18} = 13.33 m/s$$​​

2. Calculate relative speed:

​$$\text{Relative Speed} = 16.67 + 13.33 = 30$$ m/s

3. Sum of lengths of the trains:

Total Length = 240 + 270 = 510 meters

4. Calculate time to cross:

Using the formula:

Time = $$\frac{\text{Total Length}}{\text{Relative Speed}}$$​​

Substitute the values:

Time = $$\frac{510}{30} = 17$$​ seconds

Final Answer:

The trains will take 17 seconds to cross each other.