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Question

Five years ago, a woman's age was the square of her son's age. Ten years hence her age will be twice that of her son's age. Find:
(i) The age of the son five years ago.
(ii) The present age of the woman.
[4 MARKS]

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Solution

Framing the equation: 2 Marks
Answer for each subpart: 1 Mark each

Let the son's present age be y years
and the mother's present age be x years.
Then, five years ago:
Son's age was (y-5) years.
Mother's age was (x-5) years.
As per condition,
x5=(y5)2
x=(y5)2+5 ....(i)
After ten years:
Son's age would be (y+10) years.
Mother's age would be (x+10) years.
According to the question,
x + 10 = 2(y + 10)
x=2y+10....(ii)
Equating the equations (i) and (ii), we get
(y5)2+5=2y+10y210y+25+5=2y+10y212y+20=0y210y2y+20=0(y10)(y2)=0
Either y - 10 = 0 or y - 2 = 0
y=10 or y =2
According to the question, y cannot be 2.
y=10
Substituting the value of y in equation (i),
we get:
x=(105)2+5=25+5=30.
Hence, (i) Five years ago, son's age was 5 years.
(ii) Present age of the woman is 30 years.

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