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Pair of Linear Equations in Two Variables
NCERT Exemplar Ch 03
CBSE_NCERT_EXEMPLAR_CH03
Grade 10
Question:
Aruna has only Re 1 and Rs 2 coins with her. If the total number of coins that she has is $50$ and the amount of money with her is Rs $75$, then the number of Re 1 and Rs 2 coins are respectively:
$35, 15$ $35, 20$ $15, 35$ $25, 25$
Step-by-Step Solution
Key Concept: Let number of Re 1 coins be $x$ and Rs 2 coins be $y$. Equations: $x + y = 50$ and $x + 2y = 75$.
Stepwise Solution:
Subtracting $x + y = 50$ from $x + 2y = 75$: $y = 25$ (Rs 2 coins). [0.5 Mark]
Then $x = 50 - 25 = 25$ (Re 1 coins). So $(25, 25)$. [0.5 Mark]
Marking Scheme:
• Forming system of linear equations: 0.5 Mark • Solving for $x=25, y=25$: 0.5 Mark
Correct Answer:$25, 25$
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