Question

Five Years ago, a woman age was the square of her son's age. 10 years hence her age will be twice that of her son's age. Find-

1) The age of son's five years ago.
2)The present age of the women.

No Spam Answer. Answer will be with whole Calculations.

Answer 1

Hi.

Here is Your answer---

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  Let the age of the son Five years ago =  x years.
    The Present age of the son = (x + 5) years
 
Thus, The woman's age Five years ago = x^2years.
   The present age of the Woman = (x^2 + 5)Years.
   
10 years Hence,
           
         The Woman age will be = (x^2 + 5) + 10
                                                = (x^2 + 15) years.

                        Her Son's age = (x + 5) + 10
                                                = (x + 15) years.

According to the Statements,
              10 years Hence,
                 Woman's age = Twice her son's age
                         x^2 + 15 = 2( x + 15)
                         x^2 + 15 = 2x + 30
                         x^2 - 2x - 15 = 0
   
              Splitting the Middle Term,
                 
                 x^2 - 5x + 3x -15 = 0
                  x(x -5) + 3(x - 5) = 0
                    (x + 3)(x - 5) = 0

By Zero Product Rule,
      x + 3 = 0                                                   x -5 = 0
      x = -3                                                          x = 5
Since age cannot be negative, thus Rejecting x = -3 years.

Thus, the age of the son (x) = 5 years.

1) Age of the Son, Five years ago = x years
                                                       = 5 years.

2)The Present Age of the Woman = (x^2 + 5) years.
                                                       = [(5)^2 + 5] years.
                                                       = (25 + 5) years.
                                                       = 30 years.

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Hope it helps.

Have a nice day.

Answer 2

Answer:

The age of son five years ago = 5 years
The present age of the woman = 30 years.

Solution:

Let Mother's age be x and Son's age be y.

5 year's ago:
x - 5 = (y - 5)^2
=> x - 5 = y^2 - 10y + 25
=> x = y^2 - 10y + 25 + 5
=> x = y^2 - 10y + 30 ----- Equation 1

10 year's after:

x + 10 = 2(y + 10)
x + 10 = 2y + 20
x = 2y + 20 - 10
x = 2y + 10 Equation ----- 2

Apply Equation 2 into Equation 1

2y + 10 = y^2 - 10y + 30
y^2 - 10y + 30 - 2y - 10 = 0

y^2 - 12y + 20 = 0 (Its quadratic equation)

Solve the above equation we will get y value

Factors are:
(y - 10)(y - 2) = 0
y = 10, 2

So, y = 10 (The only solution that will make sense here)

Present age of Son = 10 years
The age of son five years ago = 10 - 5 = 5 years
The present age of the woman: 
x + 10 = 2(y + 10)
x + 10 = 2(10 + 10)
x = 40 - 10 = 30

The present age of the woman = 30 years.