Question

sum of ages of Father and his son is 45 years. 5 years ago, the product of their ages was 124. Determine present ages. ​

Answer 1

Answer:

Five years ago, the product of their ages was 124. The present age of son = 9 years. Hence, the present age of father be 36 years and The present age of son is 9 years

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Answer 2

Answer:

Present age of son $=9$ years

Present age of father $=36$ years .

Step-by-step explanation:

Given the relation between the ages of father and son.

It is said that sum of ages of father and son $=45$.

So let the father $=x$ and age of son $=y$ ,

then their sum $=x+y=45$

Next says that five years ago the product of their ages $=124$ .

That is, five year ago age of father $=x-5$

and that of son $=y-5$ ,

so their product $=(x-5)(y-5)=124$

         implies        

                            $xy-5x-5y+25=124\\\\xy-5x-5y=99\\\\xy-5(x+y)=99\\\\xy-5*45=99\\\\xy=99+225=324$

Now use the method of substitution.

$x+y=45$ implies $x=45-y$ .

Therefore $xy=(45-y)y=324$

                      $=45y-y^{2} =324$ .

Thus we get a quadratic equation $y^{2} -45y+324=0$

             by inspection we found that there are two numbers $-36,-9$ ,

whose sum is $-45$ and product is $324$ .

Therefore $y^{2} -45y+324=(x-36)(x-9)$

Hence the value of $x=36$  or  $x=9$

Therefore present age of son $=9$ years

and that of father $=36$ years.

Five years ago son's age $=4$ years

father's age $=31$

and $31*4=124$ .

Hence the answer.

thankyou