MathsCBSE Class 10 · Standard · Board exam 2025, set 30/6/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Standard 2025: question 37

Set in the CBSE Class 10 board exam of 2025, paper 30/6/1, section E, question 37, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q37 · 4 marks · Case-basedCompetency-basedArithmetic Progressions

In order to organise Annual Sports Day, a school prepared an eight lane running track with an integrated football field inside the track area as shown below:

The length of innermost lane of the track is 400 m and each subsequent lane is 7.6 m longer than the preceding lane.

Based on given information, answer the following questions, using concept of Arithmetic Progression.

(i)
What is the length of the 6th lane?
1 mark
(ii)
How long is the 8th lane than that of 4th lane?
1 mark
(iii)
(a) While practicing for a race, a student took one round each in first six lanes. Find the total distance covered by the student.
2 marks
OR
(iii)
(b) A student took one round each in lane 4 to lane 8. Find the total distance covered by the student.
2 marks

Figure in the paper: A running track with eight lanes (marked L1 to L8) in a stadium shape (two straight sides with semicircular ends). Inside the track is an integrated football field with the centre circle, halfway line and penalty boxes. Labels show 330'-360'/100 m-110 m (length) and 210'-240'/64 m-75 m (width). The lanes are shown as concentric tracks with the start line staggered on the left and right. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/6/1.

Hints

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

Hint 1

Write the first term and the common difference of the lane lengths.

Hint 2

Use $a_{n} = a + (n - 1) d$ for single lanes.

Hint 3

For several lanes use $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$ . For lanes 4 to 8, subtract the sum of the first 3 lanes from the sum of the first 8.

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.

The lane lengths form an AP: 400, 407.6, 415.2, … with $a = 400$ and $d = 7.6$ .
(i) $a_{6} = a + 5 d = 400 + 5 (7.6) = 438$ m.
1 mark
(ii) $a_{8} - a_{4} = (a + 7 d) - (a + 3 d) = 4 d = 4 (7.6) = 30.4$ m.
1 mark
(iii)(a) $S_{6} = \frac{6}{2} [2 a + 5 d] = 3 [2 (400) + 5 (7.6)] = 3 (838)$
1 mark
$= 2514$ m.
1 mark
(iii)(b) Distance $= S_{8} - S_{3} = \frac{8}{2} [800 + 7 (7.6)] - \frac{3}{2} [800 + 2 (7.6)] = 4 (853.2) - 1.5 (815.2)$
1 mark
$= 3412.8 - 1222.8 = 2190$ m.
1 mark

Answer: (i) 438 m; (ii) 30.4 m; (iii)(a) 2514 m; (iii)(b) 2190 m

Where the marks are

(i) $a_{6} = 438$ m (1 mark)
(ii) $a_{8} - a_{4} = 4 d = 30.4$ m (1 mark)
(iii)(a) Correct use of $S_{6}$ formula (1 mark)
(iii)(a) 2514 m (1 mark)
(iii)(b) Sets up $S_{8} - S_{3}$ (or sums $a_{4}$ to $a_{8}$ ) (1 mark)
(iii)(b) 2190 m (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 30/6/1 (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 37

Hints

Step-by-step solution

Revise the chapter

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