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Mathematics · 2025 · 3 marks
CBSE 2025 · Region 7 · Set 1 · Q27
(a) Let 2 x +5 y -1=0 and 3 x +2 y -7=0 represent the equations of two lines on which the ants are moving on the ground. Using matrix method, find a…
Let $\displaystyle 2 \mathrm{x}+5 \mathrm{y}-1=0$ and $\displaystyle 3 \mathrm{x}+2 \mathrm{y}-7=0$ represent the equations of two lines on which the ants are moving on the ground. Using matrix method, find a point common to the paths of the ants.
A shopkeeper sells $\displaystyle 50$ Chemistry, $\displaystyle 60$ Physics and $\displaystyle 35$ Maths books on day I and sells $\displaystyle 40$ Chemistry, $\displaystyle 45$ Physics and $\displaystyle 50$ Maths books on day II. If the selling price for each such subject book is ₹ $\displaystyle 150$ (Chemistry), ₹ $\displaystyle 175$ (Physics) and ₹ $\displaystyle 180$ (Maths), then find his total sale in two days, using matrix method. If cost price of all the books together is ₹ $\displaystyle 35,000$ , what profit did he earn after the sale of two days?
Marking-scheme solution
(a)
The system of equations in matrices is:
\[A X=B, \text { where } A=\left[\begin{array}{ll}
2 & 5 \\
3 & 2
\end{array}\right], X=\left[\begin{array}{l}
\mathrm{x} \\
\mathrm{y}
\end{array}\right], B=\left[\begin{array}{l}
1 \\
7
\end{array}\right]
\]
The solution is given by $\displaystyle X=A^{-1} B \Rightarrow\left[\begin{array}{l}\mathrm{x} \\
\mathrm{y}\end{array}\right]=\frac{-1}{11}\left[\begin{array}{cc} 2 & -5 \\ -3 & 2 \end{array}\right]\left[\begin{array}{l}1 \\
7\end{array}\right]=\left[\begin{array}{c}3 \\
-1\end{array}\right]$
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CBSE Class 12 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.