Pair of Linear Equations in Two Variables
CH03 Question Bank
CBSE_CH03_QUESTION_BANK
Grade 10
Question:
$5$ pens and $6$ pencils together cost Rs $9$, and $3$ pens and $2$ pencils cost Rs $5$. Find the cost of one pen and one pencil.
Step-by-Step Solution
Key Concept: Form a pair of linear equations and solve by elimination.
Let cost of a pen be Rs $x$ and a pencil be Rs $y$: $5x+6y=9$ — (1); $3x+2y=5$ — (2). [1.0 Mark]
Multiply (2) by $3$: $9x+6y=15$. Subtracting (1): $9x+6y-(5x+6y)=15-9\Rightarrow 4x=6\Rightarrow x=1.5$. [1.0 Mark]
Substituting into (2): $4.5+2y=5\Rightarrow y=0.25$. So a pen costs Rs $1.50$ and a pencil costs Rs $0.25$. [1.0 Mark]
Correct Answer:
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