Question

Mr Goel is 27 years older than her daughter Rekha. After 8 years she will be twice as old as Rekha. Find their present ages.

Answer 1

I think this help you ..
present age of Rekha= 19 years..
present age of Mr Goel=46

Answer 2

$\sf\small\underline\green{Let:-}$

$\sf{\implies The\: present\:age\:_{(Mr\:Goel)}=x}$

$\sf{\implies The\: present\:age\:_{(her\: daughter)}=y}$

$\sf\small\underline\green{To\: Find:-}$

$\sf{\implies The\: present\:age\:_{(Mr\:Goel\:and\: daughter)}=?}$

$\sf\small\underline\green{Solution:-}$

To calculate the present age of Mr Goel and her daughter, at first we have to set up equation as per the given clue in the question. Then solve the equation by solving we get the value of x and y. Here x is the present age of Mr Goel and y is the present age of his son.

$\sf\small\underline\green{Given\:in\:case\:(i):-}$

$\sf{\implies Mr\:Goel's age=His\: daughter's\:age+27}$

$\tt{\implies x=y+27--------(i)}$

$\sf\small\underline\green{Given\:in\:case\:(ii):-}$

$\sf{\implies Mr\: Goel's\:age\:_{(after\:8\: years)}=2\times\:His\: daughter's\:age\:_{(after\:8\: years)}}$

$\tt{\implies x+8=2(y+8)}$

$\tt{\implies x+8=2y+16}$

$\tt{\implies x-2y=16-8}$

$\tt{\implies x-2y=8-------(ii)}$

Putting the value of x=y+27 in eq (ii)

$\tt{\implies y+27-2y=8}$

$\tt{\implies y-2y=8-27}$

$\tt{\implies -y=-19}$

$\tt{\implies y=19}$

putting the value of y=19 in eq (i)

$\tt{\implies x=y+27}$

$\tt{\implies x=19+27}$

$\tt{\implies x=46}$

$\sf\large{Hence,}$

$\sf{\implies The\: present\:age\:_{(Mr\:Goel)}=46\: years}$

$\sf{\implies The\: present\:age\:_{(her\: daughter)}=19\: years}$