MathsCBSE Class 10 · Standard · Board exam 2026, set 30/2/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2026: question 32

Set in the CBSE Class 10 board exam of 2026, paper 30/2/1, section D, question 32, for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q32 · 5 marks · Long answerCompetency-basedPair of Linear Equations in Two Variables

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.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/2/1.

Hints

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

Hint 1

Let the prices be x and y and write one equation for each buyer.

Hint 2

Make a table of at least two integer points for each line; the meeting point of the lines gives the prices.

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.

Let the cost of 1 pencil be ₹ x and of 1 chocolate be ₹ y. Aarush: $2 x + 3 y = 11$
1 mark
Tanish: $x + 2 y = 7$
1 mark
Table for $2 x + 3 y = 11$ , i.e. $y = \frac{11 - 2 x}{3}$ : x = 1, 4, −2 gives y = 3, 1, 5. Plot (1, 3), (4, 1), (−2, 5) on graph paper and join to get a straight line.
1 mark
Table for $x + 2 y = 7$ , i.e. $y = \frac{7 - x}{2}$ : x = 1, 3, 7 gives y = 3, 2, 0. Plot (1, 3), (3, 2), (7, 0) and join to get the second line.
1 mark
The two lines intersect at (1, 3), so $x = 1$ , $y = 3$ : cost of 1 pencil = ₹ 1 and cost of 1 chocolate = ₹ 3.
1 mark

Answer: Equations: $2 x + 3 y = 11$ , $x + 2 y = 7$ ; pencil = ₹ 1, chocolate = ₹ 3

Where the marks are

Forms $2 x + 3 y = 11$ (1 mark)
Forms $x + 2 y = 7$ (1 mark)
Correct graph of $2 x + 3 y = 11$ (1 mark)
Correct graph of $x + 2 y = 7$ (1 mark)
Reads intersection: x = 1 (½ mark) and y = 3 (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 paper2026 board paper, set 30/2/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2026: question 32

Hints

Step-by-step solution

Revise the chapter

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