MathsCBSE Class 10 · Basic · Board exam 2023, set 430/1/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2023: question 32(b)

Set in the CBSE Class 10 board exam of 2023, paper 430/1/1, section D, question 32(b), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q32(b) · 5 marks · Long answerCompetency-basedQuadratic Equations

The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages (in years) was 124. Determine their present age.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/1/1.

Hints

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

Hint 1

Let the father's age be $x$ ; write the son's age using the sum 45.

Hint 2

Subtract 5 from both ages, multiply them and equate to 124; factorise $x^{2} - 45 x + 324$ .

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 father's present age be $x$ years; then son's present age $= (45 - x)$ years.
1 mark
Five years ago: father's age $= (x - 5)$ years, son's age $= (45 - x - 5) = (40 - x)$ years.
1 mark
According to the question, $(x - 5) (40 - x) = 124$ .
1 mark
$40 x - x^{2} - 200 + 5 x = 124 \Rightarrow x^{2} - 45 x + 324 = 0 \Rightarrow (x - 36) (x - 9) = 0$ .
1 mark
$x = 36$ or $x = 9$ . $x = 9$ is rejected, since then the son would be 36 years, older than the father.
½ mark
Father's present age = 36 years, son's present age = $45 - 36 = 9$ years.
½ mark

Answer: Father: 36 years, Son: 9 years

Where the marks are

Expresses present ages as $x$ and $45 - x$ (1 mark)
Writes ages five years ago (1 mark)
Forms equation $(x - 5) (40 - x) = 124$ (1 mark)
Reduces to $x^{2} - 45 x + 324 = 0$ and factorises (1 mark)
Rejects $x = 9$ (½ mark)
States father 36 years, son 9 years (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 paper2023 board paper, set 430/1/1 (Basic): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Basic 2023: question 32(b)

Hints

Step-by-step solution

Revise the chapter

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