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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?) What are their present ages? Solve graphically introducing necessary variables.

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12 years, 42 years

13 years, 47 years

18 years, 51 years

None of these

answer is A.

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Detailed Solution

Given Aftab and his daughter’s age.
Let the present age of Aftab's daughter

= x

years.
And the present age of Aftab

= y

years,

(y > x)

According to the given conditions, we have,
Seven years ago,

(y - 7) = 7 \times (x - 7)

\Rightarrow y - 7 = 7 x - 49

\Rightarrow 7 x - y - 42 = 0

……...(1)
Three years later,

(y + 3) = 3 \times (x + 3)

\Rightarrow y + 3 = 3 x + 9

\Rightarrow 3 x - y + 6 = 0

.........(2)
Thus, the algebraic relations are,

7 x - y - 42 = 0, 3 x - y + 6 = 0

.
Now, we represent the problem graphically as below:

7 x - y - 42 = 0

...(i)

3 x - y + 6 = 0

...(ii)

Plotting the points to form the lines,
Question Image

From the graph, we find that,

x = 12

and

y = 42

.
Thus, the present age of Aftab's daugther

= 12

years and the present age of Aftab

= 42

years.
Therefore, option (1) is correct.

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