MathsCBSE Class 10 · Standard · Board exam 2026, set 30/1/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Standard 2026: question 36

Set in the CBSE Class 10 board exam of 2026, paper 30/1/1, section E, question 36, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q36 · 4 marks · Case-basedCompetency-basedArithmetic Progressions

In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato. The other potatoes are arranged 3 m apart in a straight line, with a total of 10 potatoes, as shown in the figure. A competitor starts from the bucket, picks up the nearest potato, runs back to the bucket to drop it in, then returns to pick up the next potato. This process continues until all the potatoes are in the bucket.

Based on the above information, answer the following questions :

(i)
What is the distance covered to pick up the first potato and drop it in bucket ?
1 mark
(ii)
What is the distance covered to pick up the second potato and drop it in bucket ?
1 mark
(iii)(a)
What is the total distance the competitor has to run ?
2 marks
OR
(iii)(b)
If average speed of competitor is 5 m/s, then find the average time taken by competitor to put all the potatoes in the bucket.
2 marks

Figure in the paper: A bucket with potatoes at the left end of a horizontal arrow line. The distance from the bucket to the first potato is 5 m; the next nine potatoes are placed in a straight line, each 3 m apart (labelled 3m between consecutive potatoes). Total 10 potatoes. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/1/1.

Hints

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

Hint 1

Each potato needs a trip out and a trip back, so double the distance from the bucket.

Hint 2

Each next potato is 3 m farther, so each round trip grows by 6 m. That gives an AP.

Hint 3

Use $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$ with $n = 10$ . For time, divide distance by speed.

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.

(i) The first potato is 5 m from the bucket. The competitor runs 5 m to it and 5 m back:
$5 + 5 = 10 m$
1 mark
(ii) The second potato is $5 + 3 = 8$ m from the bucket. Distance there and back:
$8 + 8 = 16 m$
1 mark
(iii)(a) Each later potato is 3 m farther, so each round trip is $2 \times 3 = 6$ m longer. The round-trip distances are $10, 16, 22, \dots$
This is an AP with $a = 10$ , $d = 6$ , $n = 10$ .
1 mark
(iii)(a) $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$
$S_{10} = \frac{10}{2} [2 (10) + 9 (6)] = 5 \times 74 = 370 m$
1 mark
(iii)(b) The round-trip distances form an AP with $a = 10$ , $d = 6$ , $n = 10$ .
½ mark
(iii)(b) $S_{10} = \frac{10}{2} [2 (10) + 9 (6)] = 5 \times 74 = 370 m$
1 mark
(iii)(b) $Time = \frac{Distance}{Speed} = \frac{370}{5} = 74 seconds$
½ mark

Answer: (i) 10 m; (ii) 16 m; (iii)(a) 370 m, (iii)(b) 74 seconds

Where the marks are

(i) 10 m (1 mark)
(ii) 16 m (1 mark)
(iii)(a) Recognises an AP with $a = 10$ , $d = 6$ (1 mark)
(iii)(a) $S_{10} = 370$ m (1 mark)
(iii)(b) Identifies the AP (½ mark)
(iii)(b) Total distance 370 m (1 mark)
(iii)(b) Time = 74 s (½ mark)

Revise the chapter

Chapter: Arithmetic Progressions (notes, formulas, where marks are lost and every past question)
Topic: Word Problems and Daily Life Applications of AP

Practise this chapterBoard-style questions from Arithmetic Progressions, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 30/1/1 (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 2026: question 36

Hints

Step-by-step solution

Revise the chapter

More questions from Arithmetic Progressions