Question

Five years hence, father’s age will be three times the age of his daughter. Five years ago,

father was seven times as old as his daughter. Their present ages are:​

Answer 1

$\sf\huge \mathbb{\underline{\underline{{Solution}}}}$

Since,we don't Know their present ages so,Let assume their present ages some Variable.

Let present age of daughter be 'x'

present age of father be 'y'

Five years hence, age of daughter= x+5

Age of father = y+5

According to the question

=> y+5= 3(x+5)

=>y+5= 3x+15

=>y= 3x+10--------(1)

Five yeara ago,

Age of daughter= x-5

Age of father = y-5

According to the question

=>y-5= 7(x-5)

=>y-5=7x-35

=>y= 7x-30--------(2)

Substracting Equation 1 from 2

=>7x-30-(3x+10)= y-y

=>7x-30-3x-10=0

=>4x-40=0

=>4x= 40

=>x= 10

Put X's value into equation 1

=>y= 3x+10

=>y= 3(10)+10

=>y= 30+10=40

y=40

Therefore, Present age of daughter is 10 years

Present age of father is 40 years

Answer 2

=>y= 3x+10

=>y= 3(10)+10

=>y= 30+10=40

y=40