Rahul gets 34% of the full marks in an exam and fails by 90 marks. Rishi gets 36% of the marks in the same exam and also fails by 72 marks. What is the minimum percentage of marks a student should obtain to pass the exam.

Options

A. a.45
B. b.55
C. c.44
D. d.none of these

Answer

To solve the problem, we need to determine the minimum percentage of marks required to pass the exam based on the information given about Rahul and Rishi.

### Step-by-Step Solution:

1. **Define Variables**:
Let the total marks of the exam be \( M \).
- Rahul's score = \( 34\% \) of \( M = 0.34M \)
- Rishi's score = \( 36\% \) of \( M = 0.36M \)

2. **Set Up the Equations**:
- Rahul fails by 90 marks, which means the passing marks \( P \) can be expressed as:
\[ P = 0.34M + 90 \]
- Rishi fails by 72 marks, which gives us another equation:
\[ P = 0.36M + 72 \]

3. **Equate the Two Expressions for Passing Marks**:
Since both expressions represent the passing marks \( P \), we can set them equal to each other:
\[ 0.34M + 90 = 0.36M + 72 \]

4. **Solve for \( M \)**:
Rearranging the equation:
\[ 90 - 72 = 0.36M - 0.34M \]
\[ 18 = 0.02M \]
Now, divide both sides by \( 0.02 \):
\[ M = \frac{18}{0.02} = 900 \]

5. **Calculate Passing Marks \( P \)**:
Substitute \( M = 900 \) back into one of the equations for \( P \):
\[ P = 0.34 \times 900 + 90 \]
\[ P = 306 + 90 = 396 \]

6. **Find the Minimum Percentage to Pass**:
Now, we need to find the percentage of marks required to pass:
\[ \text{Percentage to pass} = \left(\frac{P}{M}\right) \times 100 = \left(\frac{396}{900}\right) \times 100 \]
\[ = 44\% \]

### Final Answer:
The minimum percentage of marks a student should obtain to pass the exam is **44%**.