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 :
Generated by claude-sonnet-4-6 · 2026-06-15 10:33 · grounding stimulus
Model Answer
Given: Total length = 5000 m, first pole at 200 m from base, common difference d = 150 m, last pole is 300 m from top.
The AP for pole distances from base: a = 200, d = 150.
(i) Distance of 10th pole from base:
$a_{10} = a + 9d = 200 + 9(150) = 200 + 1350 = \textbf{1550 m}$
(ii) Distance between 15th and 25th pole:
$a_{15} = 200 + 14(150) = 2300$ m
$a_{25} = 200 + 24(150) = 3800$ m
Distance = $3800 - 2300 = \textbf{1500 m}$
(iii) Time taken to reach 15th pole from the top:
Distance of 15th pole from base = 2300 m
Distance of 15th pole from top = $5000 - 2300 = 2700$ m
Time = $\dfrac{2700}{5} = \textbf{540 seconds}$
Source: Arithmetic Progressions, Case Study
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Explanation
- The AP is straightforward: a = 200, d = 150. Use $a_n = a + (n-1)d$.
- For (ii), the difference between any two consecutive 10 poles is simply $10 \times 150 = 1500$ m — a quicker check.
- For (iii), examiners expect you to find the distance from the top, not from the base. Subtract the pole's distance from the total 5000 m, then divide by speed.
- The information about "last pole 300 m from top" can be used to verify the number of poles but isn't needed for these sub-questions.