MathsCBSE Class 10 · Basic · Board exam 2025, set 430/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2025: question 27

Set in the CBSE Class 10 board exam of 2025, paper 430/5/1, section C, question 27, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q27 · 3 marks · Short answerQuadratic Equations

The sum of the squares of two consecutive even numbers is 452. Find the numbers.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/5/1.

Hints

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

Hint 1

Consecutive even numbers differ by 2, so call them $x$ and $x + 2$ .

Hint 2

Expand $x^{2} + (x + 2)^{2} = 452$ , simplify to a quadratic and factorise (look for factors of 224 that differ by 2).

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 two consecutive even numbers be $x$ and $x + 2$ .
½ mark
According to the question, $x^{2} + (x + 2)^{2} = 452 \Rightarrow 2 x^{2} + 4 x + 4 = 452 \Rightarrow x^{2} + 2 x - 224 = 0$
1 mark
$x^{2} + 16 x - 14 x - 224 = 0 \Rightarrow (x + 16) (x - 14) = 0 \Rightarrow x = 14$ or $x = - 16$
1 mark
Taking the positive even number $x = 14$ , the required numbers are 14 and 16. (If negative numbers are allowed, −16 and −14 also satisfy the condition.)
½ mark

Answer: 14 and 16

Where the marks are

Assumes numbers as $x$ and $x + 2$ (½ mark)
Forms the equation $x^{2} + 2 x - 224 = 0$ (1 mark)
Solves to get $x = 14$ (1 mark)
States the numbers 14 and 16 (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 paper2025 board paper, set 430/5/1 (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 2025: question 27

Hints

Step-by-step solution

Revise the chapter

More questions from Quadratic Equations