If a student score 43% marks then he is failed by 72 marks, but when he scores 57% marks he is passed by 40 marks. Find passing %

Options

A. 0.53
B. 0.55
C. 0.52
D. 0.5

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript.

### Step 1: Define the Variables
Let the total marks be denoted as \( X \).

### Step 2: Set Up the Equations
From the information given:
1. When the student scores 43%, he fails by 72 marks. This means:
\[ 0.43X + 72 = \text{Passing Marks} \]

2. When the student scores 57%, he passes by 40 marks. This means:
\[ 0.57X - 40 = \text{Passing Marks} \]

### Step 3: Equate the Two Expressions for Passing Marks
Since both expressions equal the passing marks, we can set them equal to each other:
\[ 0.43X + 72 = 0.57X - 40 \]

### Step 4: Rearranging the Equation
Now, we will rearrange the equation to isolate \( X \):
\[ 72 + 40 = 0.57X - 0.43X \]
\[ 112 = 0.14X \]

### Step 5: Solve for \( X \)
To find \( X \), divide both sides by 0.14:
\[ X = \frac{112}{0.14} \]
Calculating this gives:
\[ X = 800 \]

### Step 6: Find the Passing Marks
Now that we have the total marks, we can find the passing marks using either equation. Let's use the first one:
\[ \text{Passing Marks} = 0.43 \times 800 + 72 \]
Calculating this gives:
\[ \text{Passing Marks} = 344 + 72 = 416 \]

### Step 7: Calculate the Passing Percentage
Now, we can find the passing percentage:
\[ \text{Passing Percentage} = \left(\frac{\text{Passing Marks}}{X}\right) \times 100 \]
Substituting the values:
\[ \text{Passing Percentage} = \left(\frac{416}{800}\right) \times 100 \]
Calculating this gives:
\[ \text{Passing Percentage} = 52\% \]

### Final Answer
The passing percentage is **52%**.

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