Two trains can cross a pole in 9 seconds and 12 seconds respectively. Find in how much time will they cross each other if they are coming from same direction and if the speed of trains are in 5:8 ratio

Options

A. 35 sec
B. 43 sec
C. 47 sec
D. 54 sec

Answer

To solve the problem, we need to find the time taken for two trains to cross each other when they are coming from the same direction. We have the following information:

1. The first train crosses a pole in 9 seconds.
2. The second train crosses a pole in 12 seconds.
3. The speed ratio of the two trains is 5:8.

Let's break down the solution step by step.

### Step 1: Determine the lengths of the trains
To find the lengths of the trains, we can use the formula:
\[ \text{Length} = \text{Speed} \times \text{Time} \]

Let the speed of the first train be \( 5x \) and the speed of the second train be \( 8x \).

- For the first train:
\[ L_1 = \text{Speed} \times \text{Time} = 5x \times 9 = 45x \]

- For the second train:
\[ L_2 = \text{Speed} \times \text{Time} = 8x \times 12 = 96x \]

### Step 2: Calculate the relative speed
When two trains are moving in the same direction, the relative speed is given by the difference in their speeds:
\[ \text{Relative Speed} = S_2 - S_1 = 8x - 5x = 3x \]

### Step 3: Determine the total distance to be covered
When the two trains cross each other, the distance covered is the sum of their lengths:
\[ \text{Total Distance} = L_1 + L_2 = 45x + 96x = 141x \]

### Step 4: Use the formula for time
Using the formula for time, which is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
we can substitute the values we have:
\[ t = \frac{\text{Total Distance}}{\text{Relative Speed}} = \frac{141x}{3x} \]

### Step 5: Simplify the expression
Now, we can simplify the expression:
\[ t = \frac{141x}{3x} = \frac{141}{3} = 47 \text{ seconds} \]

### Conclusion
The time taken for the two trains to cross each other when coming from the same direction is **47 seconds**.

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