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Pair of Linear Equations in Two Variables
RD Sharma
CBSE
Grade 10
Question:
A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid $₹27$ for a book kept for seven days, while Susy paid $₹21$ for the book she kept for five days. Find the fixed charge and the charge for each extra day.
Step-by-Step Solution
Key Concept: Fixed charge for 3 days $= x$, extra day charge $= y$. Saritha (7 days $= 3 + 4$ extra): $x + 4y = 27$. Susy (5 days $= 3 + 2$ extra): $x + 2y = 21$. Subtract: $2y = 6 \Rightarrow y = 3, x = 15$.
Equations: (1) $x + 4y = 27$, (2) $x + 2y = 21$. [1.0 Mark] Subtract (2) from (1): $2y = 6 \Rightarrow y = ₹3$ per extra day. [1.0 Mark] $x + 2(3) = 21 \Rightarrow x = ₹15$ fixed charge. [1.0 Mark]
--- 🎯 Official CBSE Marking Scheme: Forming linear equations: 1.0 Mark Solving extra day charge $y = ₹3$: 1.0 Mark Solving fixed charge $x = ₹15$: 1.0 Mark
Correct Answer:
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