MathsCBSE Class 10 · Basic · Sample paper, session 2026-27 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic sample paper 2026-27: question 33(B)

From the official CBSE sample question paper for 2026-27, section D, question 33(B), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q33(B) · 5 marks · Long answerQuadratic Equations

John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Find the number of marbles they had with them in the beginning.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.

Hints

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

Hint 1

If John has $x$ marbles, Jivanti has $45 - x$ . Subtract 5 from each.

Hint 2

Multiply the new counts, set the product equal to 124 and solve the quadratic; both roots are valid.

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 John have $x$ marbles at the beginning; then Jivanti had $45 - x$ .
½ mark
After losing 5 each, they have $x - 5$ and $40 - x$ marbles, so $(x - 5) (40 - x) = 124$
1 mark
$40 x - x^{2} - 200 + 5 x = 124 \Rightarrow x^{2} - 45 x + 324 = 0$
½ mark
$x = \frac{45 \pm 2025 - 1296}{2} = \frac{45 \pm 27}{2}$
1 mark
$x = 36$ or $x = 9$
1 mark
Case 1: $x = 36$ , so John had 36 and Jivanti had $45 - 36 = 9$ .
½ mark
Case 2: $x = 9$ , so John had 9 and Jivanti had 36.
½ mark

Answer: 36 and 9 marbles (John 36, Jivanti 9, or John 9, Jivanti 36)

Where the marks are

Defines the variables (½ mark)
Forms $(x - 5) (40 - x) = 124$ (1 mark)
Gets $x^{2} - 45 x + 324 = 0$ (½ mark)
Applies the quadratic formula correctly (1 mark)
Gets roots 36 and 9 (1 mark)
Case 1 interpretation (½ mark)
Case 2 interpretation (½ mark)

Revise the chapter

Chapter: Quadratic Equations (notes, formulas, where marks are lost and every past question)
Topic: Word Problems on Quadratic Equations

Practise this chapterBoard-style questions from Quadratic Equations, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2026-27 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2026-27: question 33(B)

Hints

Step-by-step solution

Revise the chapter

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