Two students A and B contributed .Rs 100 towards the Prime Minister's Relief Fund to help the earthquake victims. Write a linear equation to satisfy the above data.

Options

A. `x-y=100`
B. `x+y=100`
C. `2x+y=100`
D. `x+2y=100`

Answer

To solve the problem, we need to create a linear equation based on the contributions made by students A and B towards the Prime Minister's Relief Fund.

### Step-by-Step Solution:

1. **Define the Variables**:
- Let \( X \) be the amount of money contributed by student A.
- Let \( Y \) be the amount of money contributed by student B.

2. **Set Up the Equation**:
- According to the problem, the total contribution made by both students A and B is Rs 100. Therefore, we can express this relationship as:
\[ X + Y = 100 \]

3. **Interpret the Equation**:
- The equation \( X + Y = 100 \) is a linear equation in two variables. It represents all the possible combinations of contributions by A and B that add up to Rs 100.

4. **Determine the Constraints**:
- Since contributions cannot be negative, we have the constraints:
\[ X \geq 0 \quad \text{and} \quad Y \geq 0 \]

5. **Identify Points for Graphing**:
- To graph the equation, we can find some points:
- If \( Y = 0 \), then \( X = 100 \) (Point: (100, 0))
- If \( X = 0 \), then \( Y = 100 \) (Point: (0, 100))

6. **Graph the Equation**:
- Plot the points (100, 0) and (0, 100) on a graph. Draw a straight line connecting these points. This line represents all combinations of contributions by A and B that total Rs 100.

### Final Equation:
The linear equation that satisfies the contributions of students A and B is:
\[ X + Y = 100 \]