A train is 216 m long . It crosses a platform in 19 seconds with speed 21 m/s . If some 21 m long coaches are added in train and it crosses same platform , then it takes 26 seconds to cross the platform at same speed . How many coaches were added to the train ?

Options

A. 7
B. 10
C. 12
D. 5

Explanation

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

### Step 1: Calculate the length of the platform
The train crosses the platform in 19 seconds at a speed of 21 m/s. We can use the formula:

\[ \text{Distance} = \text{Speed} \times \text{Time} \]

The total distance covered when the train crosses the platform is the length of the train plus the length of the platform.

Let \( L \) be the length of the platform. The distance covered is:

\[ \text{Distance} = 216 \, \text{m} + L \]

Using the speed and time:

\[ 216 + L = 21 \, \text{m/s} \times 19 \, \text{s} \]

Calculating the right side:

\[ 21 \times 19 = 399 \, \text{m} \]

So, we have:

\[ 216 + L = 399 \]

Now, solving for \( L \):

\[ L = 399 - 216 = 183 \, \text{m} \]

### Step 2: Set up the equation for the new train length
Now, if \( x \) coaches of length 21 m each are added to the train, the new length of the train becomes:

\[ \text{New Length} = 216 + 21x \]

The total distance covered when this new train crosses the same platform is:

\[ \text{Distance} = (216 + 21x) + 183 \]

### Step 3: Calculate the distance for the new scenario
The time taken to cross the platform with the new train is 26 seconds at the same speed of 21 m/s. Therefore, we can write:

\[ (216 + 21x) + 183 = 21 \times 26 \]

Calculating the right side:

\[ 21 \times 26 = 546 \, \text{m} \]

So we have:

\[ (216 + 21x) + 183 = 546 \]

### Step 4: Simplify the equation
Now, simplifying the left side:

\[ 399 + 21x = 546 \]

### Step 5: Solve for \( x \)
Subtract 399 from both sides:

\[ 21x = 546 - 399 \]

Calculating the right side:

\[ 21x = 147 \]

Now, divide by 21:

\[ x = \frac{147}{21} = 7 \]

### Conclusion
The number of coaches added to the train is \( 7 \).

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