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Mathematics · 2023 · 4 marks
CBSE 2023 · Region 4 · Set 3 · Q37
Two schools 'P' and 'Q' decided to award prizes to their students for two games of Hockey ₹ x per student and Cricket ₹ y per student. School 'P'…
Two schools 'P' and 'Q' decided to award prizes to their students for two games of Hockey ₹ $\displaystyle x$ per student and Cricket ₹ $\displaystyle y$ per student. School 'P' decided to award a total of ₹ $\displaystyle 9{,}500$ for the two games to $\displaystyle 5$ and $\displaystyle 4$ students respectively; while school 'Q' decided to award ₹ $\displaystyle 7{,}370$ for the two games to $\displaystyle 4$ and $\displaystyle 3$ students respectively.
[ Based on the given information, answer the following questions :
(i)
Represent the following information algebraically (in terms of $\displaystyle x$ and $\displaystyle y$ ).
(ii)
(a)
What is the prize amount for hockey ?
OR
(b)
Prize amount on which game is more and by how much ?
(iii)
What will be the total prize amount if there are $\displaystyle 2$ students each from two games ?
Marking-scheme solution
(i) \[\begin{aligned}
& 5 x+4 y=9500 \\
& 4 x+3 y=7370
\end{aligned}
\]
(ii) (a)
\[\text { (a) Solving (1) and (2), } x=980
\]
∴ Prize Amount for Hockey \(\displaystyle =₹ 980\)
OR
(ii) (b) On solving \(\displaystyle \mathrm{x}=980, \mathrm{y}=1,150\)
∴ Prize Amount for Cricket is more by ₹ \(\displaystyle (1,150-980)=₹ 170\)
(iii) \(\displaystyle 2(\mathrm{x}+\mathrm{y})=2(980+1150)=2(2130)=₹ 4,260\)
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CBSE Class 10 Mathematics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.