MathsCBSE Class 10 · Standard · Board exam 2025, set 30/3/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2025: question 33(b)

Set in the CBSE Class 10 board exam of 2025, paper 30/3/1, section D, question 33(b), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q33(b) · 5 marks · Long answerCompetency-basedArithmetic Progressions

The minimum age of children eligible to participate in a painting competition is 8 years. It is observed that the age of the youngest boy was 8 years and the ages of the participants, when seated in order of age, have a common difference of 4 months. If the sum of the ages of all the participants is 168 years, find the age of the eldest participant in the painting competition.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/3/1.

Hints

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

Hint 1

Convert 4 months into years and write the AP of ages.

Hint 2

Use the sum formula with $S_{n} = 168$ to find n. The eldest participant's age is the nth term.

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.

4 months $= \frac{4}{12} = \frac{1}{3}$ year. The ages (in years) form an AP: $8, 8 \frac{1}{3}, 8 \frac{2}{3}, 9, \dots$ with $a = 8$ and $d = \frac{1}{3}$ .
1 mark
Let there be $n$ participants. Using $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$ :
$\frac{n}{2} [16 + \frac{n - 1}{3}] = 168$
1 mark
$\frac{n ( 48 + n - 1 )}{6} = 168 \Rightarrow n^{2} + 47 n - 1008 = 0$
1 mark
$(n + 63) (n - 16) = 0 \Rightarrow n = 16$ [n cannot be negative, so reject $n = - 63$ ]
1 mark
Age of the eldest $= a_{16} = 8 + 15 \times \frac{1}{3} = 8 + 5 = 13$ years
1 mark

Answer: The eldest participant is 13 years old.

Where the marks are

Identifies the AP with $a = 8$ , $d = \frac{1}{3}$ year (1 mark)
Sets up $\frac{n}{2} [16 + (n - 1) \frac{1}{3}] = 168$ (1 mark)
Forms $n^{2} + 47 n - 1008 = 0$ (1 mark)
Solves to get $n = 16$ (1 mark)
Eldest age $= a_{16} = 13$ years (1 mark)

Revise the chapter

Chapter: Arithmetic Progressions (notes, formulas, where marks are lost and every past question)
Topic: Finding nth Term from the Sum of n Terms

Practise this chapterBoard-style questions from Arithmetic Progressions, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 30/3/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 33(b)

Hints

Step-by-step solution

Revise the chapter

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