Two trains of equal length take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?

Options

A. 16
B. 15
C. 12
D. 10

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the speed of each train
- **Train A** takes 10 seconds to cross a telegraph post. The length of Train A is 120 meters.
\[ \text{Speed of Train A} = \frac{\text{Distance}}{\text{Time}} = \frac{120 \text{ meters}}{10 \text{ seconds}} = 12 \text{ m/s} \]

- **Train B** takes 15 seconds to cross a telegraph post. The length of Train B is also 120 meters.
\[ \text{Speed of Train B} = \frac{\text{Distance}}{\text{Time}} = \frac{120 \text{ meters}}{15 \text{ seconds}} = 8 \text{ m/s} \]

### Step 2: Calculate the combined speed when trains are moving in opposite directions
When two trains are moving towards each other, their speeds add up.
\[ \text{Combined Speed} = \text{Speed of Train A} + \text{Speed of Train B} = 12 \text{ m/s} + 8 \text{ m/s} = 20 \text{ m/s} \]

### Step 3: Calculate the total distance to be covered when they cross each other
The total distance when both trains cross each other is the sum of their lengths.
\[ \text{Total Distance} = \text{Length of Train A} + \text{Length of Train B} = 120 \text{ meters} + 120 \text{ meters} = 240 \text{ meters} \]

### Step 4: Calculate the time taken to cross each other
Using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
we can calculate the time taken for the two trains to cross each other.
\[ \text{Time} = \frac{240 \text{ meters}}{20 \text{ m/s}} = 12 \text{ seconds} \]

### Final Answer
The time taken for the two trains to cross each other is **12 seconds**.

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