MathsCBSE Class 10 · Standard · Board exam 2025, set 30/2/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2025: question 31

Set in the CBSE Class 10 board exam of 2025, paper 30/2/1, section C, question 31, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q31 · 3 marks · Short answerCompetency-basedArithmetic Progressions

A sum of ₹ 2,000 is invested at 7% per annum simple interest. Calculate the interests at the end of $1^{st}$ , $2^{nd}$ and $3^{rd}$ year. Do these interests form an AP ? If so, find the interest at the end of the $2 7^{th}$ year.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/2/1.

Hints

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

Hint 1

Use $S I = \frac{P R T}{100}$ with T = 1, 2 and 3.

Hint 2

Check whether the differences between consecutive interests are equal.

Hint 3

Use $a_{n} = a + (n - 1) d$ with n = 27.

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.

Simple interest $= \frac{P \times R \times T}{100}$ .
Interest at the end of 1st year $= \frac{2000 \times 7 \times 1}{100} = ₹140$
½ mark
Interest at the end of 2nd year $= \frac{2000 \times 7 \times 2}{100} = ₹280$
½ mark
Interest at the end of 3rd year $= \frac{2000 \times 7 \times 3}{100} = ₹420$
½ mark
The interests are 140, 280, 420, …
$280 - 140 = 420 - 280 = 140$ . Yes, they form an AP with $a = 140$ and $d = 140$ .
½ mark
Using $a_{n} = a + (n - 1) d$ , interest at the end of the 27th year $= a_{27} = 140 + 26 \times 140$
½ mark
$= 140 + 3640 = ₹3780$
½ mark

Answer: ₹140, ₹280, ₹420; yes, they form an AP (d = 140); interest at the end of the 27th year = ₹3780

Where the marks are

Interest for year 1 = ₹140 (1/2 mark)
Interest for year 2 = ₹280 (1/2 mark)
Interest for year 3 = ₹420 (1/2 mark)
States they form an AP with $a = d = 140$ (1/2 mark)
Writes $a_{27} = 140 + 26 \times 140$ (1/2 mark)
Gets ₹3780 (1/2 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 30/2/1 (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 2025: question 31

Hints

Step-by-step solution

Revise the chapter

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