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Mathematics · 2025 · 4 marks
CBSE 2025 · Region 1 · Set 1 · Q36
A school is organizing a charity run to raise funds for a local hospital. The run is planned as a series of rounds around a track, with each round…
A school is organizing a charity run to raise funds for a local hospital. The run is planned as a series of rounds around a track, with each round being $\displaystyle 300$ metres. To make the event more challenging and engaging, the organizers decide to increase the distance of each subsequent round by $\displaystyle 50$ metres. For example, the second round will be $\displaystyle 350$ metres, the third round will be $\displaystyle 400$ metres and so on. The total number of rounds planned is 10.
Based on the information given above, answer the following questions :
(i)
Write the fourth, fifth and sixth term of the Arithmetic Progression so formed.
(ii)
Determine the distance of the $\displaystyle 8^{\text {th }}$ round.
(iii)
(a)
Find the total distance run after completing all $\displaystyle 10$ rounds.
OR
(b)
If a runner completes only the first $\displaystyle 6$ rounds, what is the total distance run by the runner ?
Marking-scheme solution
A.P formed is \(\displaystyle 300,350,400 \ldots \ldots\).
(i) \(\displaystyle \mathrm{a}_{4}=450\)
\[\begin{aligned}
& \mathrm{a}_{5}=500 \\
& \mathrm{a}_{6}=550
\end{aligned}
\]
(ii) \(\displaystyle \mathrm{a}_{8}=300+7 \times 50\)
\[\text { = } 650 \text { m }
\]
(iii) (a) \(\displaystyle \mathrm{S}_{10}=\frac{10}{2} \times(2 \times 300+9 \times 50)\)
\[\text { = } 5250 \mathrm{~m}
\]
(iii) (b) \(\displaystyle \mathrm{S}_{6}=\frac{6}{2} \times(2 \times 300+5 \times 50)\)
\[\text { = } 2250 \mathrm{~m}
\]
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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.