Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” Isn't this interesting? Represent this situation algebraically. Present Age of Aftab & his Daughter is.

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45 & 15

42 & 12

41 & 21

38 & 08

answer is B.

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Detailed Solution

Concept- Concept of linear equation in two variables is used. Two solve equations of two variables we will have to form two equations first.
Then, eliminate one variable to find the value of another variable. Put the value obtained in an original equation to get the value of the other variable.
Let the present age of Aftab be “A” years and the present age of his daughter be “D” years.
It is given that,
Information I:
Seven years ago
Aftab was then seven times older than his daughter.
Aftab’s age 7 years ago = (A – 7) years
Age of Aftab S daughter = (D – 7) years
A/Q
(Age of Aftab seven years ago) = 7 (Age of his daughter’s seven years ago)
(A - 7) = 7 (D - 7)
By simplifying the above equation, we get,
A−7=7D−49
Or, 7D−A=49−7
⇒ 7D−A=42  ....(i)
Information II:
Three years hence
Aftab’s age, 3 years hence = (A + 3) years.
Age of Aftab’s daughter would be = (D + 3) years.
A/Q
Aftab shall be three times older than his daughter.
(Age of Aftab after 3 years) = 3 (Age of his daughter 3 years)
⇒ (A+3) =3(D+3)
By simplifying the above equation, we get,
(A+3) =3D+9
Or,
A−3D=6 ....(ii)
Algebraic Equations involving the ages are as follows,
7D − A = 42   ...(i)
A − 3D = 6   ....(ii)
Adding equation (i) and (ii) , we get,
(7D − A) + ( A − 3D) = 42+6
By simplification, of the above equation and canceling the terms, we get,
⇒ 4D=48
further solving both sides of the above equation, we get,
⇒D=12 years
Hence, On substitution of “D = 12” in the equation (i) , we get,
7(12) −A=42
84−A=42
A=84−42
So, we get, A = 42 years.
Therefore, Aftab’s and his daughter’s ages are 42 years and 12 years respectively.
Hence, the correct answer is option 2.

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