MathsCBSE Class 10 · Standard · Board exam 2024, set 30/5/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2024: question 32(b)

Set in the CBSE Class 10 board exam of 2024, paper 30/5/1, 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 answerQuadratic Equations

The age of a man is twice the square of the age of his son. Eight years hence, the age of the man will be 4 years more than three times the age of his son. Find their present ages.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/5/1.

Hints

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

Hint 1

Let the son's present age be x; write the man's age in terms of x.

Hint 2

Add 8 to both ages and translate '4 years more than three times' into an equation.

Hint 3

Solve the quadratic and discard any value that cannot be an age.

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 present age of the son be $x$ years. Then the present age of the man $= 2 x^{2}$ years.
1 mark
After 8 years: man's age $= 2 x^{2} + 8$ , son's age $= x + 8$ . According to the question,
$2 x^{2} + 8 = 3 (x + 8) + 4$
1 mark
$2 x^{2} + 8 = 3 x + 28 \Rightarrow 2 x^{2} - 3 x - 20 = 0$
1 mark
$2 x^{2} - 8 x + 5 x - 20 = 0 \Rightarrow (2 x + 5) (x - 4) = 0 \Rightarrow x = 4$ or $x = - \frac{5}{2}$
1 mark
Age cannot be negative, so $x \neq = - \frac{5}{2}$ ; hence $x = 4$ .
½ mark
Present age of son = 4 years; present age of man $= 2 \times 4^{2} = 32$ years. (Check: after 8 years, 40 = 3 × 12 + 4 ✓)
½ mark

Answer: Son: 4 years; Man: 32 years

Where the marks are

Takes son's age x and man's age $2 x^{2}$ (1 mark)
Forms equation $2 x^{2} + 8 = 3 (x + 8) + 4$ (1 mark)
Gets $2 x^{2} - 3 x - 20 = 0$ (1 mark)
Factorises $(2 x + 5) (x - 4) = 0$ (1 mark)
Rejects negative root, x = 4 (½ mark)
States ages 4 years and 32 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 paper2024 board paper, set 30/5/1 (Standard): 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 Standard 2024: question 32(b)

Hints

Step-by-step solution

Revise the chapter

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