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Pair of Linear Equations in Two Variables
RD Sharma
CBSE
Grade 10

Question:

A student scored $40$ marks in a test, getting $3$ marks for each right answer and losing $1$ mark for each wrong answer. Had $4$ marks been awarded for each correct answer and $2$ marks been deducted for each incorrect answer, then the student would have scored $50$ marks. How many questions were there in the test?

Step-by-Step Solution

Key Concept: Right $= x$, Wrong $= y$. (1) $3x - y = 40$, (2) $4x - 2y = 50 \Rightarrow 2x - y = 25$. Subtract: $x = 15$. $y = 3(15) - 40 = 5$. Total questions $= 15 + 5 = 20$.
Equations: (1) $3x - y = 40$, (2) $2x - y = 25$. [1.0 Mark]
Subtract (2) from (1): $x = 15$ correct answers. [1.0 Mark]
$y = 3(15) - 40 = 5$ wrong answers. Total questions $= 15 + 5 = 20$. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Forming linear equations: 1.0 Mark
Solving $x = 15, y = 5$: 1.0 Mark
Finding total questions $= 20$: 1.0 Mark

Correct Answer:
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