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Mathematics · 2025 · 4 marks
CBSE 2025 · Region 4 · Set 1 · Q37
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…
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 $\displaystyle 5000$ 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 $\displaystyle 200$ m and subsequent poles are installed at equal interval of $\displaystyle 150$ m. Further, the distance of last pole from the top is $\displaystyle 300$ m. Based on above information, answer the following questions using Arithmetic Progression :
(i)
Find the distance of $\displaystyle 10^{\text {th }}$ pole from the base.
(ii)
Find the distance between $\displaystyle 15^{\text {th }}$ pole and $\displaystyle 25^{\text {th }}$ pole.
(iii)
(a)
Find the time taken by cable car to reach $\displaystyle 15^{\text {th }}$ pole from the top if it is moving at the speed of 5m/sec and coming from top.
OR
(b)
Find the total number of poles installed along the entire journey.
Marking-scheme solution
AP formed is $\displaystyle 200$, $\displaystyle 350$, 500...
(i) Distance of \(\displaystyle 10^{\text {th }}\) pole from base \(\displaystyle =a_{10}\)
\[\begin{aligned}
& =200+9 \times 150 \\
& =1550 \mathrm{~m}
\end{aligned}
\]
(ii) Distance between \(\displaystyle 15{ }^{\text {th }}\) pole and \(\displaystyle 25^{\text {th }}\) pole \(\displaystyle =a_{25}-a_{15}\)
\[=10 \times 150=1500 \mathrm{~m}
\]
(iii) (a) Distance of \(\displaystyle 15^{\text {th }}\) pole from the top \(\displaystyle =300+14 \times 150\)
\[=2400 \mathrm{~m}
\]
Time taken by cable car \(\displaystyle =\frac{2400}{5}=480\) seconds or $\displaystyle 8$ minutes
(iii) (b) Distance of last pole from the base \(\displaystyle =(5000-300) \mathrm{m}=4700 \mathrm{~m}\)
\[\therefore a_{n}=4700
\]
\(\displaystyle \Rightarrow 200+(\mathrm{n}-1) 150=4700\)
Solving, we get \(\displaystyle \mathrm{n}=31\)
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CBSE Class 10 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.