A train 220 m long passes a platform in 40 seconds. If its speed is increased by 3 m/sec, then it crosses a pole in 11 seconds. Find the length of platform.

Options

A. 380m
B. 420m
C. 350m
D. 460m

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the problem
We have a train that is 220 meters long. It passes a platform in 40 seconds. We need to find the length of the platform. Additionally, if the speed of the train is increased by 3 m/s, it crosses a pole in 11 seconds.

### Step 2: Set up the equations
1. Let the speed of the train be \( S \) m/s.
2. When the train crosses the platform, it travels a distance equal to its length plus the length of the platform (denote the length of the platform as \( P \)). Therefore, the distance traveled when crossing the platform can be expressed as:
\[ \text{Distance} = \text{Speed} \times \text{Time} \implies 220 + P = S \times 40 \]
(Equation 1)

3. When the speed of the train is increased by 3 m/s, it crosses a pole in 11 seconds. The distance traveled in this case is just the length of the train:
\[ 220 = (S + 3) \times 11 \]
(Equation 2)

### Step 3: Solve Equation 2 for S
From Equation 2:
\[ 220 = (S + 3) \times 11 \]
Dividing both sides by 11:
\[ S + 3 = \frac{220}{11} = 20 \]
Now, subtract 3 from both sides to find \( S \):
\[ S = 20 - 3 = 17 \text{ m/s} \]

### Step 4: Substitute S into Equation 1
Now that we have \( S = 17 \) m/s, we can substitute this value back into Equation 1:
\[ 220 + P = 17 \times 40 \]
Calculating the right side:
\[ 220 + P = 680 \]
Now, isolate \( P \):
\[ P = 680 - 220 = 460 \text{ meters} \]

### Conclusion
The length of the platform is \( 460 \) meters.