MathsCBSE Class 10 · Standard · Board exam 2025, set 30/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2025: question 21(a)

Set in the CBSE Class 10 board exam of 2025, paper 30/5/1, section B, question 21(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21(a) · 2 marks · Very short answerCompetency-basedPair of Linear Equations in Two Variables

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.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/5/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Turn each sentence into an equation: (kg of apples × x) + (kg of grapes × y) = total cost.

Hint 2

For consistency, compare $\frac{a _{1}}{a _{2}}$ , $\frac{b _{1}}{b _{2}}$ and $\frac{c _{1}}{c _{2}}$ .

Hint 3

If the first two ratios are equal but the third is different, the lines are parallel.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

Cost of 2 kg apples and 1 kg grapes is ₹320, so $2 x + y = 320$ ...(1)
½ mark
Cost of 4 kg apples and 2 kg grapes is ₹600, so $4 x + 2 y = 600$ ...(2)
½ mark
Comparing coefficients: $\frac{a _{1}}{a _{2}} = \frac{2}{4} = \frac{1}{2}$ , $\frac{b _{1}}{b _{2}} = \frac{1}{2}$ and $\frac{c _{1}}{c _{2}} = \frac{320}{600} = \frac{8}{15}$
½ mark
Since $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} \neq = \frac{c _{1}}{c _{2}}$ , the lines are parallel and have no common solution. Hence the system is not consistent (inconsistent).
½ mark

Answer: $2 x + y = 320$ , $4 x + 2 y = 600$ ; the system is inconsistent.

Where the marks are

Writes $2 x + y = 320$ (½ mark)
Writes $4 x + 2 y = 600$ (½ mark)
Finds the three coefficient ratios correctly (½ mark)
Concludes the system is not consistent since $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} \neq = \frac{c _{1}}{c _{2}}$ (½ mark)

Revise the chapter

Chapter: Pair of Linear Equations in Two Variables (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Pair of Linear Equations in Two Variables, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 30/5/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 21(a)

Hints

Step-by-step solution

Revise the chapter

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