MathsCBSE Class 10 · Basic · Board exam 2023, set 430/6/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2023: question 26

Set in the CBSE Class 10 board exam of 2023, paper 430/6/1, section C, question 26, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q26 · 3 marks · Short answerQuadratic Equations

The sum of the reciprocals of Varun's age (in years) 3 years ago and 5 years from now is $\frac{1}{3}$ . Find his present age.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/6/1.

Hints

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

Hint 1

Let present age be x; write his ages 3 years ago and 5 years later in terms of x.

Hint 2

Add the reciprocals, cross-multiply and form a quadratic equation.

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 Varun's present age be $x$ years. Then his age 3 years ago was $x - 3$ and 5 years from now will be $x + 5$ . According to the question: $\frac{1}{x - 3} + \frac{1}{x + 5} = \frac{1}{3}$
1 mark
$\frac{( x + 5 ) + ( x - 3 )}{( x - 3 ) ( x + 5 )} = \frac{1}{3} \Rightarrow \frac{2 x + 2}{x ^{2} + 2 x - 15} = \frac{1}{3} \Rightarrow 6 x + 6 = x^{2} + 2 x - 15 \Rightarrow x^{2} - 4 x - 21 = 0$
1 mark
$x^{2} - 7 x + 3 x - 21 = 0 \Rightarrow (x - 7) (x + 3) = 0$
½ mark
$x = 7$ or $x = - 3$ ; age cannot be negative, so $x = - 3$ is rejected. Varun's present age is 7 years.
½ mark

Answer: 7 years

Where the marks are

Forms equation $\frac{1}{x - 3} + \frac{1}{x + 5} = \frac{1}{3}$ (1 mark)
Reduces to $x^{2} - 4 x - 21 = 0$ (1 mark)
Factorises as $(x - 7) (x + 3) = 0$ (½ mark)
Rejects −3 and gives age 7 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 430/6/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2023: question 26

Hints

Step-by-step solution

Revise the chapter

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