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Pair of Linear Equations in Two Variables
RD Sharma
CBSE
Grade 10
Question:
Aruna has only $₹1$ and $₹2$ coins with her. If the total number of coins that she has is $50$ and the amount of money with her is $₹75$, then the number of $₹1$ and $₹2$ coins are, respectively: (a) $35$ and $15$ (b) $30$ and $20$ (c) $25$ and $25$ (d) $15$ and $35$
Step-by-Step Solution
Key Concept: $x + y = 50$ and $x + 2y = 75$. Subtracting gives $y = 25 \Rightarrow x = 25$.
Subtract equations: $(x + 2y) - (x + y) = 75 - 50 \Rightarrow y = 25$. [0.5 Mark] $x = 50 - 25 = 25$. Number of $₹1$ and $₹2$ coins are $25$ and $25$. [0.5 Mark]
--- 🎯 Official CBSE Marking Scheme: Solving $y = 25$: 0.5 Mark Finding $x = 25$: 0.5 Mark
Correct Answer:$25$ and $25$
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