When a student scores 28% marks then he is failed by 58 marks. But when he scores 41% marks then he is failed with 6 marks. Find passing %

Options

A. `42.5%`
B. 0.43
C. `40.66%`
D. `41.5%`

Answer

To solve the problem, we need to set up equations based on the information given about the student's scores and the marks by which he failed. Let's denote the total marks of the exam as \( T \) and the passing marks as \( P \).

### Step 1: Set up the equations based on the given information.

1. When the student scores 28% marks, he fails by 58 marks:
\[ 0.28T + 58 = P \quad \text{(Equation 1)} \]

2. When the student scores 41% marks, he fails by 6 marks:
\[ 0.41T + 6 = P \quad \text{(Equation 2)} \]

### Step 2: Set the two equations equal to each other.

Since both equations equal \( P \), we can set them equal to each other:
\[ 0.28T + 58 = 0.41T + 6 \]

### Step 3: Solve for \( T \).

Rearranging the equation to isolate \( T \):
\[ 58 - 6 = 0.41T - 0.28T \]
\[ 52 = 0.13T \]
\[ T = \frac{52}{0.13} = 400 \]

### Step 4: Substitute \( T \) back into one of the equations to find \( P \).

Using Equation 1:
\[ P = 0.28 \times 400 + 58 \]
\[ P = 112 + 58 = 170 \]

### Step 5: Calculate the passing percentage.

The passing percentage \( \%P \) can be calculated as:
\[ \%P = \left( \frac{P}{T} \right) \times 100 \]
\[ \%P = \left( \frac{170}{400} \right) \times 100 = 42.5\% \]

### Final Answer:
The passing percentage is \( 42.5\% \).

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