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Mathematics · 2025 · 4 marks
CBSE 2025 · Region 6 · Set 1 · Q37
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…
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 $\displaystyle 400$ m and each subsequent lane is $\displaystyle 7.6$ 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 $\displaystyle 6^{\text {th }}$ lane ?
(ii)
How long is the $\displaystyle 8^{\text {th }}$ lane than that of $\displaystyle 4^{\text {th }}$ lane ?
(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.
OR
(b)
A student took one round each in lane $\displaystyle 4$ to lane 8. Find the total distance covered by the student.
Marking-scheme solution
Here AP is \(\displaystyle 400,407.6,415.2, \ldots\)
(i) \(\displaystyle a_{6}=400+5(7.6)=438 \mathrm{~m}\)
(ii) \(\displaystyle a_{8}-a_{4}=30.4 \mathrm{~m}\)
(iii) \(\displaystyle \mathrm{S}_{6}=\frac{6}{2}(2 \times 400+5 \times 7.6)\)
\[=2514 \mathrm{~m}
\]
OR
(iii) Total distance covered \(\displaystyle =\mathrm{S}_{8}-\mathrm{S}_{3}\)
\[\begin{aligned}
& =\frac{8}{2}(2 \times 400+7 \times 7.6)-\frac{3}{2}(2 \times 400+2 \times 7.6) \\
& =2190 \mathrm{~m}
\end{aligned}
\]
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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.