A students gets 60% of the maximum marks. If he gets 50% more than the passing mark, then the passing mark is-what percentage of the maximum marks?

Options

A. 75%
B. 40
C. `37.5%`
D. 50%

Answer

To solve the problem step by step, let's denote the maximum marks as \( M \) and the passing marks as \( P \).

### Step 1: Determine the marks obtained by the student.
The student scores 60% of the maximum marks, which can be expressed as:
\[ \text{Marks obtained} = 0.6M \]

### Step 2: Relate the marks obtained to the passing marks.
According to the problem, the marks obtained by the student (which is \( 0.6M \)) is 50% more than the passing marks. This can be expressed as:
\[ 0.6M = P + 0.5P \]
This simplifies to:
\[ 0.6M = 1.5P \]

### Step 3: Solve for the passing marks in terms of maximum marks.
To find \( P \), we can rearrange the equation:
\[ P = \frac{0.6M}{1.5} \]
Calculating this gives:
\[ P = \frac{0.6}{1.5}M = 0.4M \]

### Step 4: Calculate the percentage of passing marks with respect to maximum marks.
To find the passing marks as a percentage of the maximum marks, we can express this as:
\[ \text{Percentage of passing marks} = \left( \frac{P}{M} \right) \times 100 \]
Substituting \( P = 0.4M \):
\[ \text{Percentage of passing marks} = \left( \frac{0.4M}{M} \right) \times 100 = 40\% \]

### Final Answer:
The passing mark is **40%** of the maximum marks.

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