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Pair of Linear Equations in Two Variables
CH03 Question Bank
CBSE_CH03_QUESTION_BANK
Grade 10
Question:
A fraction becomes $\dfrac{9}{11}$ if $2$ is added to both its numerator and denominator. It becomes $\dfrac56$ if $3$ is added to both. Find the fraction.
Step-by-Step Solution
Key Concept: Let the fraction be $x/y$; translate both conditions into linear equations and solve.
Let the fraction be $\dfrac{x}{y}$. From the first condition: $\dfrac{x+2}{y+2}=\dfrac{9}{11}\Rightarrow 11x+22=9y+18\Rightarrow 11x-9y=-4$ — (1). [1.0 Mark]
From the second condition: $\dfrac{x+3}{y+3}=\dfrac{5}{6}\Rightarrow 6x+18=5y+15\Rightarrow 6x-5y=-3$ — (2). [1.0 Mark]
Multiply (1) by $5$ and (2) by $9$: $55x-45y=-20$ and $54x-45y=-27$. Subtracting: $x=7$. Substituting into (2): $42-5y=-3\Rightarrow y=9$. The fraction is $\dfrac{7}{9}$. [1.0 Mark]
Correct Answer:
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