Question

The sum of present age of father and his son is 45 than 5 years ago the productof age was 34 find their present age

Answer 1

Answer:

Let father’s age be x years and let that of the son be y years.

Now, x+y=45

and,(x-5)(y-5)=34

So,xy -5x-5y+25=34

xy-5(x+y)+25=34

xy-5(45)+25=34

xy-225+25=34

xy=34–25+225

xy=9+225

xy=234

Now, x+y=45 and xy=234

and, 234’s factors are 1,2,3,6,9,13,18,26,39,78,117,234.

We need to find two factors which when added give 45 and when multiplied, give 234.

Clearly, 39 and 6 are two such numbers. { 39+6=45 and 39 x 6=234}

So, x=39 and y=6

Thus father’s age is 39 years and that of the son is 6 years. { father is always older than son}

Answer 2

Answer:

Let the age of son be x year

        so, father age =(45-x)

age of son 5 years ago =(x-5) year

age of father 5 years ago=(45-x-5)

                                          =(40-x) year

A.t.q

       (x-5)(40-x)=34

       x^2-45x+234=0

       x^2-39x-6x+234=0

       x(x-39)-6(x-39)=0

       (x-39)(x-6)=0

        x=6

present age of son=6 years

present age of father=39 years