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Mathematics · 2024 · 4 marks
CBSE 2024 · Region 4 · Set 1 · Q37
Treasure Hunt is an exciting and adventurous game where participants follow a series of clues/numbers/maps to discover hidden treasures. Players…
Treasure Hunt is an exciting and adventurous game where participants follow a series of clues/numbers/maps to discover hidden treasures. Players engage in a thrilling quest, solving puzzles and riddles to unveil the location of the coveted prize. While playing a treasure hunt game, some clues (numbers) are hidden in various spots collectively forming an A.P. If the number on the $\displaystyle \mathrm{n}^{\text {th }}$ spot is $\displaystyle 20+4 \mathrm{n}$, then answer the following questions to help the players in spotting the clues :
(i)
Which number is on first spot ?
(ii)
(a)
Which spot is numbered as $\displaystyle 112$ ?
OR
(b)
What is the sum of all the numbers on the first $\displaystyle 10$ spots ?
(iii)
Which number is on the $\displaystyle (\mathrm{n}-2)^{\text {th }}$ spot ?
Marking-scheme solution
(i) Number on the first spot \(\displaystyle =20+4 \times 1=24\)
(ii) (a)
\[\begin{aligned}
& 20+4 n=112 \\
& \Rightarrow n=23
\end{aligned}
\]
OR
(ii) (b)
\[\begin{aligned}
\mathrm{d} & =4 \\
S_{10} & =\frac{10}{2}[2 \times 24+9 \times 4] \\
& =420
\end{aligned}
\]
(iii) \[\begin{aligned}
\text { Number on the }(n-2)^{\text {th }} \text { spot } & =20+4(n-2) \\
& =12+4 n
\end{aligned}
\]
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CBSE Class 10 Mathematics past-paper question from the 2024 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.