Question

Sum of the ages of father and son is38years. 6 years ago the product of their ages was 25 find their present ages?​

Answer 1

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Sum of the ages of father and son is38years. 6 years ago the product of their ages was 25 find their present ages?

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Given:

Sum of the ages of father and son is38 years.

6 years ago the product of their ages was 25.

To find:

find their present ages ?

Solution:

Let father's present age be ' x ' years.

.°. Son's present age = 38 - x

Six years ago, the age of father was ( x - 6 ) years

and the age of son was = (38 - x - 6) =( 32 - x ) years

As, six years ago, the product of ages was 25

Therefore,

$\sf{:\implies (x-6)(32-x)=25}$

$\sf{:\implies 32x-x^{2}-192+6x=25}$

$\sf{:\implies -x^{2}+38x-192-25=0}$

$\sf{:\implies -x^{2}+38x-217=0}$

$\sf{:\implies -(x^{2}-38x+217)=0}$

$\sf{:\implies x^{2}-38x+217=0}$

$\sf{:\implies x^{2}-(31+7)x+217=0}$

$\sf{:\implies x^{2}-31x-7x+217=0}$

$\sf{:\implies x(x-31)-7(x-31)=0}$

$\sf{:\implies (x-31)(x-7)=0}$

$\sf{:\implies x = 31}$

or x = 7

but , x cannot be 7

$\boxed{\bf{\pink{.°.\:\:x\:\:=31}}}$

Therefore,

Father's present age = 31 years

Son's present age = (38 - 31) = 7 years

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