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Mathematics · 2024 · 5 marks
CBSE 2024 · Region 2 · Set 1 · Q32
Using graphical method, solve the following system of equations : \[3 x+y+4=0 \text { and } 3 x-y+2=0 \]Tara scored $\displaystyle 40$ marks in a test, getting $\displaystyle 3$ marks for each right answer and losing $\displaystyle 1$ mark for each wrong answer. Had $\displaystyle 4$ marks been awarded for each correct answer and $\displaystyle 2$ marks been deducted for each wrong answer, then Tara would have scored $\displaystyle 50$ marks. Assuming that Tara attempted all questions, find the total number of questions in the test.
Using graphical method, solve the following system of equations : \[3 x+y+4=0 \text { and } 3 x-y+2=0 \]
Tara scored $\displaystyle 40$ marks in a test, getting $\displaystyle 3$ marks for each right answer and losing $\displaystyle 1$ mark for each wrong answer. Had $\displaystyle 4$ marks been awarded for each correct answer and $\displaystyle 2$ marks been deducted for each wrong answer, then Tara would have scored $\displaystyle 50$ marks. Assuming that Tara attempted all questions, find the total number of questions in the test.
Marking-scheme solution
Correct solution \(\displaystyle \mathbf{x}=-\mathbf{1}, \mathbf{y}=-\mathbf{1}\)
Let number of correct answers be x and number of incorrect answers be y
\[\begin{aligned}
& 3 x-y=40 \\
& 4 x-2 y=50
\end{aligned}
\]
Solving, we get \(\displaystyle \mathrm{x}=15, \mathrm{y}=5\)
∴ Total number of questions \(\displaystyle =20\)
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CBSE Class 10 Mathematics past-paper question from the 2024board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.