156.5 m long train, travelling at 57 km/hr, crosses a platform in 39 seconds. What is the length of the platform?
(a)613.5m
(b)476m
(c)586m
(d)461m

Options

A. 613.5 m
B. 476 m
C. 586 m
D. 461 m

Answer

To find the length of the platform that a train crosses, we can use the formula for distance, which is:

**Distance = Speed × Time**

### Step-by-Step Solution:

1. **Identify the given values:**
- Length of the train (L_train) = 156.5 m
- Speed of the train (V_train) = 57 km/hr
- Time taken to cross the platform (T) = 39 seconds

2. **Convert the speed from km/hr to m/s:**
- To convert km/hr to m/s, we use the conversion factor:
\[ 1 \text{ km/hr} = \frac{5}{18} \text{ m/s} \]
- Therefore,
\[ V_{train} = 57 \times \frac{5}{18} = \frac{285}{18} \approx 15.83 \text{ m/s} \]

3. **Calculate the total distance covered by the train while crossing the platform:**
- The total distance (D_total) covered by the train while crossing the platform is the sum of the length of the train and the length of the platform (L_platform):
\[ D_{total} = L_{train} + L_{platform} \]

4. **Use the distance formula:**
- According to the distance formula:
\[ D_{total} = V_{train} \times T \]
- Substituting the values we have:
\[ D_{total} = 15.83 \text{ m/s} \times 39 \text{ s} = 617.37 \text{ m} \]

5. **Set up the equation:**
- We know that:
\[ D_{total} = L_{train} + L_{platform} \]
- Thus:
\[ 617.37 = 156.5 + L_{platform} \]

6. **Solve for the length of the platform:**
- Rearranging the equation gives us:
\[ L_{platform} = 617.37 - 156.5 = 460.87 \text{ m} \]

7. **Round to the nearest meter:**
- Rounding 460.87 m gives us approximately 461 m.

### Conclusion:
The length of the platform is approximately **461 m**, which corresponds to option (d).