A train running at the speed of 72 kmph crosses a pole in 30 seconds. Find the time taken by the same train to cross the pole with the speed of 54 kmph (in sec)?

Options

A. A)42
B. B)48
C. C)54
D. D)40

Answer

To solve the problem, we need to find the time taken by a train to cross a pole at a different speed. Here’s a step-by-step solution:

### Step 1: Understand the Problem
The train crosses a pole, which means it travels a distance equal to its own length. We need to use the information given about the speed and time taken to find the length of the train.

### Step 2: Calculate the Length of the Train
The train's speed is given as 72 km/h and it crosses the pole in 30 seconds. First, we need to convert the speed from km/h to m/s.

- **Conversion Factor**: 1 km/h = (1000 m / 3600 s) = 5/18 m/s
- **Convert 72 km/h to m/s**:
\[ 72 \text{ km/h} = 72 \times \frac{5}{18} = 20 \text{ m/s} \]

Now, we can find the length of the train using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Substituting the values:
\[ \text{Length of the train} = 20 \text{ m/s} \times 30 \text{ s} = 600 \text{ m} \]

### Step 3: Calculate the Time to Cross the Pole at 54 km/h
Now we need to find out how long it takes for the same train (600 m long) to cross a pole at a speed of 54 km/h.

- **Convert 54 km/h to m/s**:
\[ 54 \text{ km/h} = 54 \times \frac{5}{18} = 15 \text{ m/s} \]

Now we can use the distance formula again to find the time taken to cross the pole:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Substituting the values:
\[ \text{Time} = \frac{600 \text{ m}}{15 \text{ m/s}} = 40 \text{ seconds} \]

### Final Answer
The time taken by the train to cross the pole at a speed of 54 km/h is **40 seconds**.

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