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

let rekha's present age be x

therefore, mrs goel's present age is x+27

after 8 yrs...

rekha's age=x+8

mrs goel's age=x+27+8

according to the problem....

2(x+8)=x+27+8

2x+16=x+35

2x-x=35-16

x=19

rekha's present age=x=19yrs

therefore mrs goel's present age=x+27=(19+27)yrs=46yrs

Answer 2

$\huge{\bold{\blue{Solution:}}}$

Let the present age of Rekha be $\bold{x}$ years.

Present age of Mr. Goel = $\bold{(x + 27)}$ years

Rekha's age after $8$ years = $\bold{(x + 8)}$ years.

Mrs. Goel's age after $8$ years
= $\bold{(x + 27 + 8)}$ years

= $\bold{(x + 35)}$ years

According to the question

= > $\large{\fbox{\bold{x + 35 = 2(x + 8)}}}$

= > $\large{\fbox{\bold{x + 35 = 2x + 16}}}$

= > $\large{\fbox{\bold{2x - x = 35 - 16}}}$

= > $\large{\fbox{\bold{x = 19}}}$

Rekha's present age $\bold{ = 19}$ years

Therefore, Mrs. Goel's present age
= $\bold{(19 + 27)}$ years

$\huge{\fbox{\bold{= 46 \: years}}}$

$\large{\bold{\red{Hope\:it\:works\: !!! \:}}}$