MathsCBSE Class 10 · Basic · Sample paper, session 2024-25 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic sample paper 2024-25: question 32(A)

From the official CBSE sample question paper for 2024-25, section D, question 32(A), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q32(A) · 5 marks · Long answerQuadratic Equations

Amita buys some books for ₹1920. If she had bought 4 more books for the same amount each book would cost her ₹ 24 less. How many books did she buy? What was the initial price of one book?

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

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

Hint 1

If she buys $x$ books, each costs $\frac{1920}{x}$ . Write the cost per book when she buys $x + 4$ books.

Hint 2

The difference of the two costs is ₹24. Clear the fractions to get a quadratic.

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 number of books bought be $x$ . Then the cost of one book is $₹ \frac{1920}{x}$ .
1 mark
With $x + 4$ books, each costs $₹ \frac{1920}{x + 4}$ . So:
$\frac{1920}{x} - \frac{1920}{x + 4} = 24$
1 mark
$1920 \times \frac{( x + 4 ) - x}{x ( x + 4 )} = 24 \Rightarrow 7680 = 24 x (x + 4) \Rightarrow x^{2} + 4 x - 320 = 0$
$(x + 20) (x - 16) = 0$
1 mark
$x = 16$ or $x = - 20$ . The number of books cannot be negative, so $x = 16$ . Amita bought 16 books.
1 mark
Initial price of one book $= \frac{1920}{16} = ₹120$ .
1 mark

Answer: 16 books; ₹120 per book

Where the marks are

Writes the cost of one book as $\frac{1920}{x}$ (1 mark)
Forms the equation $\frac{1920}{x} - \frac{1920}{x + 4} = 24$ (1 mark)
Reduces to $x^{2} + 4 x - 320 = 0$ and factorises (1 mark)
Rejects $- 20$ and gets 16 books (1 mark)
Price of one book = ₹120 (1 mark)

Revise the chapter

Chapter: Quadratic Equations (notes, formulas, where marks are lost and every past question)
Topic: Standard Form of a Quadratic Equation

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 2024-25 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2024-25: question 32(A)

Hints

Step-by-step solution

Revise the chapter

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