MathsCBSE Class 10 · Basic · Board exam 2025, set 430/2/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2025: question 28(b)

Set in the CBSE Class 10 board exam of 2025, paper 430/2/1, section C, question 28(b), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q28(b) · 3 marks · Short answerCompetency-basedPair of Linear Equations in Two Variables

An academy offering cricket coaching bought 10 bats and 5 balls for $₹ 32, 500$ . Later, the academy bought 2 bats and 8 balls for $₹ 10, 000$ . If there is no change in the cost of the bat and of the ball, find the cost of 1 bat and 1 ball.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/2/1.

Hints

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

Hint 1

Let the costs of one bat and one ball be x and y and write one equation for each purchase.

Hint 2

Simplify the first equation by dividing by 5, then eliminate x.

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 cost of 1 bat = ₹ $x$ and cost of 1 ball = ₹ $y$ . Then $10 x + 5 y = 32500$ , i.e. $2 x + y = 6500$ ...(i)
1 mark
and $2 x + 8 y = 10000$ ...(ii)
1 mark
Subtracting (i) from (ii): $7 y = 3500 \Rightarrow y = 500$ . Then $2 x = 6500 - 500 = 6000 \Rightarrow x = 3000$ .
1 mark
Cost of 1 bat = ₹3000 and cost of 1 ball = ₹500.

Answer: 1 bat = ₹3000, 1 ball = ₹500

Where the marks are

Forms equation $10 x + 5 y = 32500$ (1 mark)
Forms equation $2 x + 8 y = 10000$ (1 mark)
Finds $x = 3000$ and $y = 500$ (½ + ½ marks)

Revise the chapter

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

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 430/2/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 28(b)

Hints

Step-by-step solution

Revise the chapter

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