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Mathematics · 2026 · 5 marks
CBSE 2026 · Region 5 · Set 3 · Q32
Three students A, B and C go to a book-store to buy art books, story books and puzzle solving books. A buys one of each type of book for a total of ₹…
Three students A, B and C go to a book-store to buy art books, story books and puzzle solving books. A buys one of each type of book for a total of ₹ $\displaystyle 21$ . B buys $\displaystyle 4$ art books, $\displaystyle 3$ story books and $\displaystyle 2$ puzzle solving books for ₹ $\displaystyle 60$ . C buys $\displaystyle 6$ art books, $\displaystyle 2$ story books and $\displaystyle 3$ puzzle solving books and pays ₹ $\displaystyle 10$ more than B . Use matrix method to find the cost of each type of book.
Marking-scheme solution
Let cost of one art book, one story book, one puzzle solving book be ₹ x, ₹ y and ₹ z respectively
$\displaystyle x+y+z=21$; $\displaystyle 4 x+3 y+2 z=60$; $\displaystyle 6 x+2 y+3 z=70$
Let $\displaystyle A=\begin{bmatrix} 1 & 1 & 1 \\ 4 & 3 & 2 \\ 6 & 2 & 3 \end{bmatrix}, X=\begin{bmatrix} x \\ y \\ z \end{bmatrix}, B=\begin{bmatrix} 21 \\ 60 \\ 70 \end{bmatrix}$
$\displaystyle |A|=-5 \neq 0 \Rightarrow A^{-1}$ exists
System becomes $\displaystyle A X=B$. So, $\displaystyle X=A^{-1} B$
$\displaystyle \operatorname{adj} A=\begin{bmatrix} 5 & -1 & -1 \\ 0 & -3 & 2 \\ -10 & 4 & -1 \end{bmatrix}$
$\displaystyle A^{-1}=\dfrac{1}{-5}\begin{bmatrix} 5 & -1 & -1 \\ 0 & -3 & 2 \\ -10 & 4 & -1 \end{bmatrix}$
$\displaystyle X=\dfrac{1}{-5}\begin{bmatrix} 5 & -1 & -1 \\ 0 & -3 & 2 \\ -10 & 4 & -1 \end{bmatrix}\begin{bmatrix} 21 \\ 60 \\ 70 \end{bmatrix}$
$\displaystyle X=\begin{bmatrix} 5 \\ 8 \\ 8 \end{bmatrix}$
$\displaystyle \therefore$ cost of one art book, one story book, one puzzle solving book is ₹ $\displaystyle 5$, ₹ $\displaystyle 8$ and ₹ $\displaystyle 8$ respectively
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CBSE Class 12 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.