Sabarmati express takes 18 seconds to pass completely through a satation 162 m long and 15 seconds through another station 120 m long the length of the Sabarmati express is:

Options

A. 132 m
B. 100 m
C. 80 m
D. 90 m

Answer

To find the length of the Sabarmati Express, we can use the information given about the time it takes for the train to pass through two different stations.

### Step 1: Understand the problem
We know:
- The time taken to pass the first station (162 m) is 18 seconds.
- The time taken to pass the second station (120 m) is 15 seconds.

Let the length of the Sabarmati Express be \( L \) meters.

### Step 2: Calculate the speed of the train
The speed of the train can be calculated using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

### Step 3: Set up the equations
1. For the first station:
- The distance the train travels while passing the station = Length of the train + Length of the station = \( L + 162 \)
- Time taken = 18 seconds
- Speed = \( \frac{L + 162}{18} \)

2. For the second station:
- The distance the train travels while passing the station = Length of the train + Length of the station = \( L + 120 \)
- Time taken = 15 seconds
- Speed = \( \frac{L + 120}{15} \)

### Step 4: Set the speeds equal to each other
Since the speed of the train remains constant, we can set the two expressions for speed equal to each other:
\[ \frac{L + 162}{18} = \frac{L + 120}{15} \]

### Step 5: Cross-multiply to solve for \( L \)
Cross-multiplying gives us:
\[ 15(L + 162) = 18(L + 120) \]

### Step 6: Expand both sides
Expanding both sides:
\[ 15L + 2430 = 18L + 2160 \]

### Step 7: Rearrange the equation
Rearranging gives:
\[ 2430 - 2160 = 18L - 15L \]
\[ 270 = 3L \]

### Step 8: Solve for \( L \)
Dividing both sides by 3:
\[ L = 90 \]

### Conclusion
The length of the Sabarmati Express is **90 meters**.

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