Question

sum of the present ages of friends is 23 tears, five years ago product of their ages was 42.find their ages 5 years hence​

Answer 1

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Answer 2

Answer:

16 years and 17 years

Step-by-step explanation:

Consider the present age of friend A is = $x$ year

Consider the present age of friend B is = $y$ year

As per the problem, Sum of their present age is =23 years

$\therefore(x+y)=23\\\\x=23-y....................\text{equation-1}$

Five years ago age of the friend A was =$(x-5)$ years

Five years ago age of the friend B was =$(y-5)$ years

As per the problem, Five years ago product of their age were =42 years

$\therefore(x-5)\times(y-5)=42\\\\\Rightarrow(23-y-5)(y-5)=42\\\\\Rightarrow(18-y)(y-5)=42\\\\\Rightarrow(18y-90-y^{2}+5y)=42\\\\\Rightarrow(23y-90-y^{2})=42\\\\\Rightarrow(42-23y+90+y^{2})=0\\\\\Rightarrow(y^{2}-23y+132)=0\\\\\Rightarrow(y^{2}-12y-11y+132)=0\\\\\Rightarrow y(y-12)-11(y-12)=0\\\\\Rightarrow (y-12)(y-11)=0$

As $(y-12)(y-11)=0$

therefore $y=11$ or $y=12$

If $y=11$ then $x=23-y=23-11=12$

If $y=12$ then $x=23-y=23-12=11$

therefore the present age of the two friends are 11 years and 12 years

therefore the age of the two friends after five years are $(11+5)=16$ years and $(12+5)=17$ years