Two students appeared at an examination. One of them secured 9 marks more than the other and his marks were 56% of the sum of their marks. The marks obtained by them are:

Options

A. A) 42, 33
B. B) 43, 34
C. C) 41, 32
D. D) 39, 30

Answer

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

### Step 1: Define the variables
Let the marks obtained by student B be \( x \). Since student A secured 9 marks more than student B, the marks obtained by student A will be \( x + 9 \).

**Hint:** Start by defining the variables for the unknowns in the problem.

### Step 2: Set up the equation based on the given percentage
According to the problem, the marks of student A are 56% of the sum of their marks. The sum of their marks can be expressed as:
\[ \text{Sum of marks} = x + (x + 9) = 2x + 9 \]
Thus, we can write the equation:
\[ x + 9 = 0.56(2x + 9) \]

**Hint:** Use the information given in the problem to form an equation.

### Step 3: Simplify the equation
Now, we can simplify the equation:
\[ x + 9 = 0.56(2x + 9) \]
Expanding the right side:
\[ x + 9 = 1.12x + 5.04 \]

**Hint:** Distribute the percentage to the sum to get a clearer equation.

### Step 4: Rearrange the equation
Now, let's rearrange the equation to isolate \( x \):
\[ x - 1.12x = 5.04 - 9 \]
This simplifies to:
\[ -0.12x = -3.96 \]
Dividing both sides by -0.12 gives:
\[ x = \frac{-3.96}{-0.12} = 33 \]

**Hint:** Move all terms involving \( x \) to one side and constant terms to the other side.

### Step 5: Find the marks of both students
Now that we have \( x = 33 \), we can find the marks for both students:
- Marks of student B (x) = 33
- Marks of student A (x + 9) = 33 + 9 = 42

**Hint:** Substitute back to find the values of both variables.

### Step 6: State the final answer
The marks obtained by the two students are:
- Student A: 42 marks
- Student B: 33 marks

**Hint:** Clearly state the final results for clarity.

### Final Answer:
The marks obtained by them are 42 and 33.