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

Options

A. `35%`
B. `45%`
C. `40%`
D. `48%`

Answer

To solve the problem step by step, we will break down the information provided and calculate the minimum passing percentage.

### Step 1: Determine the Passing Marks
Rajesh scored 112 marks, which was 32 more than the passing marks. We can express this relationship mathematically:

\[ P + 32 = 112 \]

Where \( P \) is the passing marks. Rearranging the equation gives us:

\[ P = 112 - 32 \]

Calculating this gives:

\[ P = 80 \]

### Step 2: Relate Sonal's Marks to Passing Marks
Sonal scored 75% of the maximum marks, which was 70 more than the passing marks. We can express this as:

\[ 0.75M = P + 70 \]

Where \( M \) is the maximum marks. Substituting \( P = 80 \) into the equation gives:

\[ 0.75M = 80 + 70 \]

Calculating this gives:

\[ 0.75M = 150 \]

### Step 3: Calculate Maximum Marks
To find \( M \), we can rearrange the equation:

\[ M = \frac{150}{0.75} \]

Calculating this gives:

\[ M = 200 \]

### Step 4: Calculate Minimum Passing Percentage
Now that we have both the passing marks \( P \) and the maximum marks \( M \), we can calculate the minimum passing percentage using the formula:

\[ \text{Minimum Passing Percentage} = \left(\frac{P}{M}\right) \times 100 \]

Substituting the values we found:

\[ \text{Minimum Passing Percentage} = \left(\frac{80}{200}\right) \times 100 \]

Calculating this gives:

\[ \text{Minimum Passing Percentage} = 40\% \]

### Final Answer
The minimum passing percentage of the test is **40%**.

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