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Mathematics · 2024 · 4 marks
CBSE 2024 · Region 3 · Set 1 · Q38
A scholarship is a sum of money provided to a student to help him or her pay for education. Some students are granted scholarships based on their…
A scholarship is a sum of money provided to a student to help him or her pay for education. Some students are granted scholarships based on their academic achievements, while others are rewarded based on their financial needs.
Every year a school offers scholarships to girl children and meritorious achievers based on certain criteria. In the session $\displaystyle 2022$-$\displaystyle 23$, the school offered monthly scholarship of ₹ $\displaystyle 3,000$ each to some girl students and ₹ $\displaystyle 4,000$ each to meritorious achievers in academics as well as sports. In all, $\displaystyle 50$ students were given the scholarships and monthly expenditure incurred by the school on scholarships was $\displaystyle ₹ 1,80,000$. Based on the above information, answer the following questions :
(i)
Express the given information algebraically using matrices.
(ii)
Check whether the system of matrix equations so obtained is consistent or not.
(iii)
(a)
Find the number of scholarships of each kind given by the school, using matrices.
OR
(b)
Had the amount of scholarship given to each girl child and meritorious student been interchanged, what would be the monthly expenditure incurred by the school?
Marking-scheme solution
Let No. of girl child scholarships $\displaystyle =\mathrm{x}$
No. of meritorious achievers $\displaystyle =\mathrm{y}$
$\displaystyle \mathrm{x}+\mathrm{y}=50$
$\displaystyle 3000 \mathrm{x}+4000 \mathrm{y}=180000$ or $\displaystyle 3 \mathrm{x}+4 \mathrm{y}=180$
$\displaystyle \left[\begin{array}{ll} 1 & 1 \\ 3 & 4 \end{array}\right]\left[\begin{array}{l}\mathrm{x} \\
\mathrm{y}\end{array}\right]=\left[\begin{array}{c}50 \\
180\end{array}\right]$
$\displaystyle \left|\begin{array}{ll} 1 & 1 \\ 3 & 4 \end{array}\right|=1 \neq 0$
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CBSE Class 12 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.