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,
x−5=(y−5)2
⇒x=(y−5)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
(y−5)2+5=2y+10⇒y2−10y+25+5=2y+10⇒y2−12y+20=0⇒y2−10y−2y+20=0⇒(y−10)(y−2)=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=(10−5)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.