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

CBSE Class 10 Mathematics Standard 2025: question 37

Set in the CBSE Class 10 board exam of 2025, paper 30/4/1, 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

Cable cars at hill stations are one of the major tourist attractions. On a hill station, the length of cable car ride from base point to top most point on the hill is 5000 m. Poles are installed at equal intervals on the way to provide support to the cables on which car moves.

The distance of first pole from base point is 200 m and subsequent poles are installed at equal interval of 150 m. Further, the distance of last pole from the top is 300 m.

Based on above information, answer the following questions using Arithmetic Progression :

(i)
Find the distance of $1 0^{th}$ pole from the base.
1 mark
(ii)
Find the distance between $1 5^{th}$ pole and $2 5^{th}$ pole.
1 mark
(iii)(a)
Find the time taken by cable car to reach $1 5^{th}$ pole from the top if it is moving at the speed of 5 m/sec and coming from top.
2 marks
OR
(iii)(b)
Find the total number of poles installed along the entire journey.
2 marks

Figure in the paper: Illustration of cable cars hanging from a cable supported by several poles on a hill slope; the cars travel along the cable between the base and the top station. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/4/1.

Hints

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

Hint 1

Write the distances of successive poles from the base as an AP and identify $a$ and $d$ .

Hint 2

The difference between two terms of an AP is (difference in positions) × $d$ . When coming from the top, start the AP at 300 m.

Hint 3

For the number of poles, find how far the last pole is from the base and solve $a_{n} = a + (n - 1) d$ for $n$ .

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 distances of the poles from the base form an AP 200, 350, 500, … with $a = 200$ and $d = 150$ .
(i) $a_{10} = a + 9 d = 200 + 9 \times 150 = 1550$ m
1 mark
(ii) $a_{25} - a_{15} = (a + 24 d) - (a + 14 d) = 10 d = 10 \times 150 = 1500$ m
1 mark
(iii)(a) Counting from the top, the poles are at distances 300, 450, 600, … from the top (an AP with $a = 300$ , $d = 150$ ).
Distance of the 15th pole from the top $= 300 + 14 \times 150 = 2400$ m
1 mark
(iii)(a) Time $= \frac{distance}{speed} = \frac{2400}{5} = 480$ s, i.e. 8 minutes.
1 mark
(iii)(b) Distance of the last pole from the base $= 5000 - 300 = 4700$ m, so $a_{n} = 4700$ .
½ mark
(iii)(b) $200 + (n - 1) \times 150 = 4700 \Rightarrow (n - 1) \times 150 = 4500 \Rightarrow n - 1 = 30$
1 mark
(iii)(b) $n = 31$ , so 31 poles are installed.
½ mark

Answer: (i) 1550 m; (ii) 1500 m; (iii)(a) 480 s (8 minutes); (iii)(b) 31 poles

Where the marks are

Finds $a_{10} = 200 + 9 \times 150 = 1550$ m (1 mark)
Finds $a_{25} - a_{15} = 10 d = 1500$ m (1 mark)
(iii)(a) Distance of the 15th pole from the top $= 300 + 14 \times 150 = 2400$ m (1 mark)
(iii)(a) Time $= \frac{2400}{5} = 480$ s (1 mark)
(iii)(b) Last pole is 4700 m from the base (½ mark)
(iii)(b) Forms $200 + (n - 1) 150 = 4700$ (1 mark)
(iii)(b) Gets $n = 31$ (½ 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 30/4/1 (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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