If a train travelling at 54 kmph crosses a boy stand - ing on a platform in 12 s and the platform in 26 s, then what is the length of the platform ?

Answer

To find the length of the platform, we can break down the problem into a series of steps.

### Step-by-Step Solution:

1. **Convert the speed of the train from km/h to m/s**:
- The speed of the train is given as 54 km/h.
- To convert km/h to m/s, we use the formula:
\[ \text{Speed in m/s} = \text{Speed in km/h} \times \frac{5}{18} \]
- Calculation:
\[ 54 \times \frac{5}{18} = 15 \text{ m/s} \]

2. **Calculate the length of the train (LT)**:
- The train crosses a boy standing on the platform in 12 seconds.
- The distance covered when crossing the boy is equal to the length of the train.
- Using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
- Calculation:
\[ LT = 15 \text{ m/s} \times 12 \text{ s} = 180 \text{ meters} \]

3. **Calculate the total distance when the train crosses the platform**:
- The train crosses the platform in 26 seconds.
- The total distance covered while crossing the platform is the sum of the length of the train and the length of the platform (LP).
- Using the same distance formula:
\[ \text{Total Distance} = \text{Speed} \times \text{Time} \]
- Calculation:
\[ \text{Total Distance} = 15 \text{ m/s} \times 26 \text{ s} = 390 \text{ meters} \]

4. **Calculate the length of the platform (LP)**:
- We know that the total distance covered is the length of the train plus the length of the platform:
\[ \text{Total Distance} = LT + LP \]
- Rearranging gives us:
\[ LP = \text{Total Distance} - LT \]
- Substituting the values:
\[ LP = 390 \text{ meters} - 180 \text{ meters} = 210 \text{ meters} \]

### Final Answer:
The length of the platform is **210 meters**.

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