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Pair of Linear Equations in Two Variables
NCERT Exemplar
CBSE
Grade 10
Question:
The father's age is six times his son's age. Four years hence, the age of the father will be four times his son's age. The present ages (in years) of the son and the father are respectively: (a) $4, 24$ (b) $6, 36$ (c) $5, 30$ (d) $3, 18$
Step-by-Step Solution
Key Concept: Let son's age be $x$ and father's age be $y$. Equations: $y = 6x$ and $y + 4 = 4(x + 4)$.
Substitute $y = 6x$ into $y + 4 = 4x + 16$: $6x + 4 = 4x + 16 \Rightarrow 2x = 12 \Rightarrow x = 6$. [0.5 Mark] Father's age $y = 6(6) = 36$. Present ages are $6$ and $36$. [0.5 Mark]
--- 🎯 Official CBSE Marking Scheme: Setting up age equations: 0.5 Mark Solving for present ages (6 and 36): 0.5 Mark
Correct Answer:$6, 36$
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