Abhishek got 432 marks in a test which were 112 more than that of Arun marks, If Sonakshi got `60%` marks out of total mark of the test which were 64 mark more than the Arun marks. What percent of marks did Arun got?

Options

A. A)`65%`
B. B)`60%`
C. C)`45%`
D. D)`50%`

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Determine Arun's Marks
We know that Abhishek got 432 marks, which is 112 more than Arun's marks. We can set up the equation:

\[ \text{Abhishek's Marks} = \text{Arun's Marks} + 112 \]

Substituting the known value:

\[ 432 = \text{Arun's Marks} + 112 \]

To find Arun's marks, we subtract 112 from 432:

\[ \text{Arun's Marks} = 432 - 112 = 320 \]

### Step 2: Determine Sonakshi's Marks
According to the problem, Sonakshi got 60% of the total marks, and her marks were 64 more than Arun's marks. Therefore, we can express Sonakshi's marks as:

\[ \text{Sonakshi's Marks} = \text{Arun's Marks} + 64 \]

Substituting the value we found for Arun's marks:

\[ \text{Sonakshi's Marks} = 320 + 64 = 384 \]

### Step 3: Calculate Total Marks
Since Sonakshi's marks (384) represent 60% of the total marks, we can set up the equation:

\[ \text{Sonakshi's Marks} = 60\% \text{ of Total Marks} \]

Let the total marks be \( T \). Thus, we can write:

\[ 384 = 0.6T \]

To find \( T \), we divide both sides by 0.6:

\[ T = \frac{384}{0.6} = 640 \]

### Step 4: Calculate Arun's Percentage of Total Marks
Now that we know the total marks (640), we can calculate the percentage of marks Arun got:

\[ \text{Percentage of Arun's Marks} = \left( \frac{\text{Arun's Marks}}{\text{Total Marks}} \right) \times 100 \]

Substituting the values we have:

\[ \text{Percentage of Arun's Marks} = \left( \frac{320}{640} \right) \times 100 \]

Calculating this gives:

\[ \text{Percentage of Arun's Marks} = 0.5 \times 100 = 50\% \]

### Final Answer
Arun got **50%** of the total marks.

---