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Mathematics · Pair of Linear Equations in Two Variables · NCERT Examples

Example 5

A complete, independently verified solution for NCERT Example 5.

Mathematics · Chapter 3 · NCERT Examples

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NCERT Example

Example 5

substitution method · graphical method · age problem

Seven years ago Aftab was seven times his daughter’s age; three years from now he will be three times her age. Represent and solve the situation.

Solution

Let s and t be their present ages.

s−7=7(t−7)⇒s−7t+42=0s-7=7(t-7)\Rightarrow s-7t+42=0
s+3=3(t+3)⇒s−3t=6s+3=3(t+3)\Rightarrow s-3t=6
s=3t+6⇒3t+6−7t+42=0s=3t+6\Rightarrow3t+6-7t+42=0
t=12,s=42t=12,\qquad s=42
AgesHorizontal axis t; vertical axis s. The lines intersect at (12, 42).s − 7t + 42 = 0s − 3t = 6(12, 42)
Horizontal axis t; vertical axis s. The lines intersect at (12, 42).

The ages become 35 and 5 seven years ago, and 45 and 15 three years later.

Final answer

Aftab is 42 and his daughter is 12.