Pair of Linear Equations in Two Variables
NCERT Exemplar
CBSE
Grade 10
Question:
Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu now?
Step-by-Step Solution
Key Concept: Let present ages be $x$ (Nuri) and $y$ (Sonu). Form equations: $x - 5 = 3(y - 5)$ and $x + 10 = 2(y + 10)$.
Condition 1 (5 yrs ago): $x - 5 = 3(y - 5) \Rightarrow x - 5 = 3y - 15 \Rightarrow x - 3y = -10$ -- (eq 1). [1.0 Mark]
Condition 2 (10 yrs later): $x + 10 = 2(y + 10) \Rightarrow x + 10 = 2y + 20 \Rightarrow x - 2y = 10$ -- (eq 2). [1.0 Mark]
Subtract eq 1 from eq 2: $(x - 2y) - (x - 3y) = 10 - (-10) \Rightarrow y = 20$.
Substitute $y = 20$ into eq 2: $x - 40 = 10 \Rightarrow x = 50$.
Present ages: Nuri is $50$ years old, Sonu is $20$ years old. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Forming equation 1 ($x - 3y = -10$): 1.0 Mark
Forming equation 2 ($x - 2y = 10$): 1.0 Mark
Solving for Nuri = 50 yrs, Sonu = 20 yrs: 1.0 Mark
Correct Answer:
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