The cost of 2 kg apples and 1 kg of grapes on a day was found to be ₹ 320. The cost of 4 kg apples and 2 kg grapes was found to be ₹ 600. If cost of 1 kg of apples and 1 kg of grapes is ₹ $x$ and ₹ y respectively, represent the given situation algebraically as a system of equations and check whether the system so obtained is consistent or not.
Generated by claude-sonnet-4-6 · 2026-06-15 10:34 · grounding rag
Model Answer
The two equations are:
$$2x + y = 320 \quad \text{...(1)}$$
$$4x + 2y = 600 \quad \text{...(2)}$$
Comparing ratios: $\dfrac{a_1}{a_2} = \dfrac{2}{4} = \dfrac{1}{2}$, $\dfrac{b_1}{b_2} = \dfrac{1}{2}$, $\dfrac{c_1}{c_2} = \dfrac{320}{600} = \dfrac{8}{15}$
Since $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}$, the system is inconsistent (no solution).
Source: Chapter 3, Section 3.4 Summary
Explanation
- Form both equations directly from the given information using x and y.
- Compare the three ratios $\frac{a_1}{a_2}$, $\frac{b_1}{b_2}$, $\frac{c_1}{c_2}$ to decide consistency.
- The middle condition ($a_1/a_2 = b_1/b_2 \neq c_1/c_2$) always means inconsistent (parallel lines, no solution). State this conclusion clearly for full marks.