In a test, Rajesh got 112 marks which is 32 more than the passing marks. Sonal got 75% marks which is 70 more than the passing marks. What is the minimum passing percentage of the test?

Options

A. 35
B. 45
C. 40
D. 30

Answer

To solve the problem step by step, we will first determine the passing marks based on the information given about Rajesh and Sonal's scores.

**Step 1: Determine the passing marks from Rajesh's score.**
- Rajesh scored 112 marks, which is 32 marks more than the passing marks.
- Let the passing marks be \( P \).
- According to the information given, we can write the equation:
\[ 112 = P + 32 \]
- Rearranging the equation to find \( P \):
\[ P = 112 - 32 = 80 \]

**Step 2: Determine the passing marks from Sonal's score.**
- Sonal scored 75% of the total marks, which is also 70 marks more than the passing marks.
- Let the total marks be \( T \).
- Sonal's score can be expressed as:
\[ 0.75T = P + 70 \]
- Substituting \( P = 80 \) into the equation:
\[ 0.75T = 80 + 70 \]
\[ 0.75T = 150 \]

**Step 3: Solve for the total marks \( T \).**
- To find \( T \), divide both sides of the equation by 0.75:
\[ T = \frac{150}{0.75} = 200 \]

**Step 4: Calculate the passing percentage.**
- The passing percentage is calculated using the formula:
\[ \text{Passing Percentage} = \left( \frac{P}{T} \right) \times 100 \]
- Substituting the values of \( P \) and \( T \):
\[ \text{Passing Percentage} = \left( \frac{80}{200} \right) \times 100 = 40\% \]

Thus, the minimum passing percentage of the test is **40%**.

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