A student scores 15% & failed by 30 marks while another student who scores 50% get 40 marks more than minimum required marks to pass. Find the maximum marks in the exam ?

Options

A. 150
B. 175
C. 200
D. 225

Answer

To solve the problem step by step, we will denote the maximum marks in the exam as \( M \).

### Step 1: Understand the scores of the students
- The first student scores 15% of the maximum marks \( M \).
- The second student scores 50% of the maximum marks \( M \).

### Step 2: Set up equations based on the information given
1. The first student failed by 30 marks. This means that if the passing marks are \( P \), then:
\[ 0.15M + 30 = P \]
2. The second student scored 40 marks more than the passing marks. Therefore:
\[ 0.50M - 40 = P \]

### Step 3: Set the two equations equal to each other
Since both expressions equal \( P \), we can set them equal to each other:
\[ 0.15M + 30 = 0.50M - 40 \]

### Step 4: Solve for \( M \)
1. Rearranging the equation gives:
\[ 30 + 40 = 0.50M - 0.15M \]
\[ 70 = 0.35M \]
2. Now, divide both sides by 0.35 to find \( M \):
\[ M = \frac{70}{0.35} \]
\[ M = 200 \]

### Conclusion
The maximum marks in the exam is \( 200 \).

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