A student got 20% marks and failed by 72 marks. If he scores 40% marks then he gets 8 marks more than the passing marks. Find the passing marks.

Options

A. 150
B. 152
C. 142
D. 160

Answer

To solve the problem, we need to find the passing marks based on the information given about the student's scores.

### Step 1: Define Variables
Let the total marks be represented as \( T \). According to the problem, the student scored 20% of the total marks and failed by 72 marks.

### Step 2: Set Up the Equation for 20% Marks
The marks obtained by the student can be expressed as:
\[ \text{Marks obtained} = 0.2T \]
Since the student failed by 72 marks, we can express the passing marks \( P \) as:
\[ P = 0.2T + 72 \]

### Step 3: Set Up the Equation for 40% Marks
If the student scores 40% of the total marks, then:
\[ \text{Marks obtained at 40%} = 0.4T \]
According to the problem, if the student scores 40%, he gets 8 marks more than the passing marks:
\[ 0.4T = P + 8 \]

### Step 4: Substitute the Expression for Passing Marks
Now, we can substitute the expression for \( P \) from Step 2 into the equation from Step 3:
\[ 0.4T = (0.2T + 72) + 8 \]

### Step 5: Simplify the Equation
Now, simplify the equation:
\[ 0.4T = 0.2T + 80 \]
Subtract \( 0.2T \) from both sides:
\[ 0.4T - 0.2T = 80 \]
\[ 0.2T = 80 \]

### Step 6: Solve for Total Marks
Now, solve for \( T \):
\[ T = \frac{80}{0.2} = 400 \]

### Step 7: Find the Passing Marks
Now that we have the total marks, we can find the passing marks \( P \):
Using the equation \( P = 0.2T + 72 \):
\[ P = 0.2 \times 400 + 72 = 80 + 72 = 152 \]

### Final Answer
The passing marks are:
\[ \boxed{152} \]