Question:

1. Introduce variables\
Let \(A\) be Aftab's present age (in years) and \(D\) be his daughter's present age.\
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2. Form the first equation (seven years ago)\
\(\text{Seven years ago, Aftab's age}=A-7\)\
\(\text{Daughter's age seven years ago}=D-7\)\
According to the statement, \(A-7 = 7\,(D-7)\).\
Simplify:\
\[A-7 = 7D - 49\]\
\[A = 7D - 42\] ...(i)\
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3. Form the second equation (three years from now)\
\(\text{Aftab's age after 3 years}=A+3\)\
\(\text{Daughter's age after 3 years}=D+3\)\
The condition gives \(A+3 = 3\,(D+3)\).\
Simplify:\
\[A+3 = 3D + 9\]\
\[A = 3D + 6\] ...(ii)\
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4. Solve the system by substitution\
From (i) and (ii) we have two expressions for \(A\):\
\[7D - 42 = 3D + 6\]\
Bring like terms together:\
\[7D - 3D = 6 + 42\]\
\[4D = 48\]\
\[D = 12\] years (daughter's present age).\
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5. Find Aftab's age using either (i) or (ii). Using (ii):\
\[A = 3D + 6 = 3\times12 + 6 = 42\] years.\
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6. Verification\
- Seven years ago: Aftab = \(42-7 = 35\), Daughter = \(12-7 = 5\). Indeed, \(35 = 7\times5\).\
- After three years: Aftab = \(42+3 = 45\), Daughter = \(12+3 = 15\). Indeed, \(45 = 3\times15\).\
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7. Graphical representation\
- Plot the two straight lines given by \(A = 7D - 42\) and \(A = 3D + 6\) on a coordinate plane where the \(x\)-axis represents the daughter's age \(D\) and the \(y\)-axis represents Aftab's age \(A\).\
- The lines intersect at the point \((D, A) = (12, 42)\). This intersection point gives the solution of the system, i.e., the present ages of Aftab and his daughter.