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

Let the marks obtained by the two students be \( x \) and \( y \), where \( x > y \).

We are given two key pieces of information:
1. One student (let's assume \( x \)) secured 9 marks more than the other, i.e.
   \[
   x = y + 9
   \]
2. The marks of this student were 56% of the sum of their marks, i.e.
   \[
   x = 0.56(x + y)
   \]

Now we can solve this system of equations step by step.

### Step 1: Substitute the value of \( x \) from the first equation into the second equation.
\[
y + 9 = 0.56((y + 9) + y)
\]
Simplify the equation:
\[
y + 9 = 0.56(2y + 9)
\]
\[
y + 9 = 1.12y + 5.04
\]

### Step 2: Solve for \( y \).
Subtract \( 1.12y \) from both sides:
\[
y - 1.12y = 5.04 - 9
\]
\[
-0.12y = -3.96
\]
Divide by \( -0.12 \):
\[
y = \frac{-3.96}{-0.12} = 33
\]

### Step 3: Find \( x \).
Substitute \( y = 33 \) into the first equation:
\[
x = 33 + 9 = 42
\]

### Conclusion:
The marks obtained by the two students are:
- One student got 42 marks.
- The other student got 33 marks.

Would you like more details on this, or do you have any questions?

Here are 5 related questions to consider:
1. How would the problem change if the percentage was 60% instead of 56%?
2. Can you express this problem using matrices?
3. What if the difference in marks was 12 instead of 9?
4. How can you check if the percentage of marks obtained by the higher scorer is correct?
5. How would the solution change if both students had scored equal marks?

**Tip:** Always carefully translate word problems into equations, keeping track of variables and relationships between them.

Explore this algebra problem where two students' marks are compared. Learn how to solve for their marks using linear equations and percentage calculations. Ideal for students in Grades 8-10.

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