Question

Two sections, A and B, of class X contributed a total of Rs. 1500 for the Uttarakhand flood victims. The contribution from X-A was Rs. 100 less than that of X-B. Graphically, find the amounts contributed by both sections.

Hint:

When solving graphical questions, choose coordinate points that are clean multiples of 100 so that plotting on standard grid paper is simple and highly accurate.

Answer 1

Step 1: Understanding the Question:
Let the contribution of section X-A be Rs. $X$ and section X-B be Rs. $Y$.
We are given two conditions:
1. The total contribution from both sections is Rs. 1500.
2. The contribution from X-A is Rs. 100 less than that of X-B.
We need to find the values of $X$ and $Y$ graphically.

Step 2: Key Formula or Approach:
1. Translate the problem into a pair of linear equations:
- From condition 1:
\[ X + Y = 1500 \quad \text{--- (Equation 1)} \]
- From condition 2:
\[ X = Y - 100 \implies Y - X = 100 \quad \text{--- (Equation 2)} \]
2. Find coordinates (ordered pairs) for each equation to plot on the graph.
3. The point where the two lines intersect represents the solution to the system.

Step 3: Detailed Explanation:

• 1. Find coordinate points for Equation 1 ($X + Y = 1500$):
- If $X = 700$, then $Y = 1500 - 700 = 800$. Point: $P_1(700, 800)$.
- If $X = 500$, then $Y = 1500 - 500 = 1000$. Point: $P_2(500, 1000)$.
- If $X = 800$, then $Y = 1500 - 800 = 700$. Point: $P_3(800, 700)$.

• 2. Find coordinate points for Equation 2 ($Y - X = 100 \implies Y = X + 100$):
- If $X = 700$, then $Y = 700 + 100 = 800$. Point: $Q_1(700, 800)$.
- If $X = 500$, then $Y = 500 + 100 = 600$. Point: $Q_2(500, 600)$.
- If $X = 600$, then $Y = 600 + 100 = 700$. Point: $Q_3(600, 700)$.

• 3. Graph plotting and finding intersection:
- Plot the points on a graph paper with suitable scale (e.g., 1 cm = 100 units on both axes).
- Draw straight lines connecting the plotted points for both equations.
- Observe that both straight lines intersect at the point $(700, 800)$.
- This intersection point is the common solution: $X = 700$ and $Y = 800$.
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Step 4: Final Answer:
The amount contributed by section X-A is Rs. 700 and by section X-B is Rs. 800.