Aarush bought 2 pencils and 3 chocolates for ₹ 11 and Tanish bought 1 pencil and 2 chocolates for ₹ 7 from the same shop. Represent this situation in the form of a pair of linear equations. Find the price of 1 pencil and 1 chocolate, graphically.
Generated by claude-sonnet-4-6 · 2026-06-15 10:34 · grounding rag
Model Answer
Let the price of 1 pencil = ₹x and price of 1 chocolate = ₹y.
Pair of linear equations:
Aarush: $2x + 3y = 11$ ... (1)
Tanish: $x + 2y = 7$ ... (2)
Table of values:
For eq. (1): $2x + 3y = 11$
| x | 1 | 4 |
|---|---|---|
| y | 3 | 1 |
Points: A(1, 3), B(4, 1)
For eq. (2): $x + 2y = 7$
| x | 1 | 3 |
|---|---|---|
| y | 3 | 2 |
Points: P(1, 3), Q(3, 2)
Graph: Plot and join points A, B for line (1) and P, Q for line (2) on graph paper.
Result: The two lines intersect at (1, 3).
∴ x = 1, y = 3
Price of 1 pencil = ₹1; Price of 1 chocolate = ₹3.
Source: Chapter 3, Section 3.2 (Graphical Method)
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Explanation
- First 1 mark: forming the two correct equations.
- Next 2 marks: making value tables and plotting correctly on the graph.
- Last 2 marks: identifying the intersection point and stating the answer clearly.
- Always verify: 2(1) + 3(3) = 11 ✓ and 1 + 2(3) = 7 ✓.
- Write the final answer as a sentence — examiners look for it explicitly.