MathsCBSE Class 10 · Standard · Sample paper, session 2026-27 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard sample paper 2026-27: question 28(B)

From the official CBSE sample question paper for 2026-27, section C, question 28(B), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q28(B) · 3 marks · Short answerArithmetic Progressions

Find the sum of integers between 1 and 400 that are multiples of 4 as well as of 5.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.

Hints

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

Hint 1

A number that is a multiple of both 4 and 5 is a multiple of their LCM.

Hint 2

List the multiples of 20 that lie strictly between 1 and 400 as an A.P. Find how many terms there are, then use $S_{n} = \frac{n}{2} (a + l)$ .

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.

A number that is a multiple of both 4 and 5 is a multiple of LCM(4, 5) = 20.
Such numbers between 1 and 400 form the A.P. $20, 40, 60, \dots, 380$ . (400 is not included, since we need numbers between 1 and 400.)
1 mark
Here $a = 20$ and $d = 20$ . Let $a_{n} = 380$ :
$20 + (n - 1) \times 20 = 380$ .
½ mark
$\Rightarrow (n - 1) \times 20 = 360 \Rightarrow n = 19$ .
½ mark
Using $S_{n} = \frac{n}{2} (a + l)$ : $S_{19} = \frac{19}{2} (20 + 380)$ .
½ mark
$S_{19} = \frac{19}{2} \times 400 = 3800$ .
½ mark

Answer: 3800

Where the marks are

Identifies the A.P. $20, 40, \dots, 380$ of multiples of 20 (1 mark)
Sets up $a_{n} = 20 + (n - 1) 20 = 380$ (½ mark)
Finds $n = 19$ (½ mark)
Applies the sum formula $S_{19} = \frac{19}{2} (20 + 380)$ (½ mark)
Gets 3800 (½ mark)

Revise the chapter

Chapter: Arithmetic Progressions (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Arithmetic Progressions, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2026-27 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard sample paper 2026-27: question 28(B)

Hints

Step-by-step solution

Revise the chapter

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