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: Translate the conditions into two equations, as before.
Let $X$ be the contribution of X-A and $Y$ be the contribution of X-B, both in rupees.
\[ X + Y = 1500 \quad \text{(total contribution)} \] \[ Y - X = 100 \quad \text{(X-A gave Rs.\ 100 less than X-B)} \]
Step 2: Solve algebraically first, using elimination, to know exactly where the two lines should cross.
Add the two equations directly so that $X$ cancels out:
\[ (X + Y) + (Y - X) = 1500 + 100 \] \[ 2Y = 1600 \implies Y = 800 \] Substitute back:
\[ X = 1500 - Y = 1500 - 800 = 700 \] So we expect the two lines to cross exactly at the point $(700, 800)$ before we even draw them.

Step 3: Rewrite both equations in slope-intercept form to choose easy plotting points.
\[ Y = 1500 - X \qquad \text{(slope } -1\text{)} \] \[ Y = X + 100 \qquad \text{(slope } 1\text{)} \] Since the two lines have slopes $-1$ and $1$, one falling and one rising, they must cross at exactly one point, which our algebra says is $(700, 800)$.

Step 4: Pick two points on each line and draw them on graph paper.
For $Y = 1500 - X$: if $X = 500$, $Y = 1000$; if $X = 900$, $Y = 600$.
For $Y = X + 100$: if $X = 500$, $Y = 600$; if $X = 900$, $Y = 1000$.
Using a scale such as 1 cm = 100 units on both axes, plot these points, draw both straight lines, and confirm visually that they meet exactly at $(700, 800)$, matching our algebraic prediction.

Final Answer:
The amount contributed by section X-A is Rs. 700 and by section X-B is Rs. 800. \[ \boxed{X = 700,\ Y = 800} \]