What is the speed of the train ?
(i) the train crosses a signal pole in 18 seconds.
(ii) The train crosses a platform of equal length in 36 seconds.
(iii) Length of the train is 330 metres.

Options

A. (i) and (ii) only
B. (ii) and (iii) only
C. (i) & (iii) only
D. (iii) and either (i) or (ii)

Answer

To find the speed of the train, we can use the information provided in the statements. Let's solve it step by step.

### Step 1: Understand the Problem
We need to find the speed of the train. The speed is calculated using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

### Step 2: Analyze Statement (i)
Statement (i) states that the train crosses a signal pole in 18 seconds.
- When a train crosses a signal pole, the distance covered is equal to the length of the train.
- We do not have the length of the train from this statement alone.

### Step 3: Analyze Statement (ii)
Statement (ii) states that the train crosses a platform of equal length in 36 seconds.
- Here, the distance covered is the sum of the lengths of the train and the platform. Since the platform is of equal length to the train, if we denote the length of the train as \( L \), the distance covered is \( L + L = 2L \).
- We still do not have the length of the train from this statement alone.

### Step 4: Analyze Statement (iii)
Statement (iii) provides the length of the train, which is 330 meters.
- Now we can use this information to calculate the speed.

### Step 5: Calculate Speed Using Statement (i) and (iii)
Using Statement (i) and (iii):
- Length of the train \( L = 330 \) meters
- Time taken to cross the signal pole = 18 seconds

Using the formula for speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{330 \text{ meters}}{18 \text{ seconds}} \]

Calculating this gives:
\[ \text{Speed} = \frac{330}{18} \approx 18.33 \text{ m/s} \]

### Step 6: Calculate Speed Using Statement (ii) and (iii)
Using Statement (ii) and (iii):
- The total distance covered when crossing the platform is \( 2L = 2 \times 330 = 660 \) meters.
- Time taken to cross the platform = 36 seconds.

Using the formula for speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{660 \text{ meters}}{36 \text{ seconds}} \]

Calculating this gives:
\[ \text{Speed} = \frac{660}{36} = 18.33 \text{ m/s} \]

### Conclusion
From both methods, we find that the speed of the train is approximately 18.33 m/s.