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Pair of Linear Equations in Two Variables
NCERT Exemplar Ch 03
CBSE_NCERT_EXEMPLAR_CH03
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:

$4, 24$
$6, 36$
$5, 30$
$3, 18$

Step-by-Step Solution

Key Concept: Let son's age be $x$ and father's age be $y$. Equations: $y = 6x$ and $y + 4 = 4(x + 4)$.
Stepwise Solution:

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]

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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