In the morning batch at Lamamia we have observed that when five-five students took seat on a bench, 4 students remained unseated. But when eleven students took seat per bench, 4 benches remained vaccant. The number of students in our morning batch were?

Options

A. 55
B. 48
C. 26
D. none of these

Answer

To solve the problem, we need to set up equations based on the information provided.

Let:
- \( x \) = total number of students in the morning batch
- \( y \) = total number of benches

### Step 1: Create the first equation based on the first scenario
According to the problem, when 5 students sit on each bench, 4 students remain unseated. This can be expressed as:
\[ x = 5y + 4 \]
This equation states that the total number of students \( x \) is equal to the number of students seated (which is \( 5 \times y \)) plus the 4 students who are unseated.

### Step 2: Create the second equation based on the second scenario
In the second scenario, when 11 students sit on each bench, 4 benches remain vacant. This can be expressed as:
\[ x = 11(y - 4) \]
This equation states that the total number of students \( x \) is equal to the number of students seated (which is \( 11 \times (y - 4) \)) since \( y - 4 \) is the number of benches that are occupied.

### Step 3: Set the two equations equal to each other
Now we have two equations:
1. \( x = 5y + 4 \)
2. \( x = 11(y - 4) \)

Since both expressions equal \( x \), we can set them equal to each other:
\[ 5y + 4 = 11(y - 4) \]

### Step 4: Solve for \( y \)
Now, let's simplify and solve for \( y \):
\[ 5y + 4 = 11y - 44 \]
Rearranging gives:
\[ 4 + 44 = 11y - 5y \]
\[ 48 = 6y \]
\[ y = 8 \]

### Step 5: Substitute \( y \) back to find \( x \)
Now that we have \( y \), we can substitute it back into one of the original equations to find \( x \). We'll use the first equation:
\[ x = 5y + 4 \]
Substituting \( y = 8 \):
\[ x = 5(8) + 4 \]
\[ x = 40 + 4 \]
\[ x = 44 \]

### Conclusion
The total number of students in the morning batch is \( \boxed{44} \).