Question

The present age of father is four times the age of his daughter. After 10 years, the age of father will become three times the age of his daughter. Find their present age.

Answer 1

$\text{ Let \: \: the \: \: present \: \: age \: \: of \: \: daughter \: \: is \: \: x \: years, } \\ \text{ So, \: present \: \: age \: \: of \: \: father \: \: will \: \: be \: \: 4x \: years \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [ four \: times \: of \: daughter's \: age \: as \: discussed \: in \: the \: question ] }$



$\bold{After \: \: 1 0 \: \: years, \: \: Age \: \: of \: \: daughter = ( x + 10 ) \: years } \\ \mathbf{ \: Age \: \: of \: \: father = ( 4x + 10 ) \: years }$



But according to the question,


After of father after 10 years = 3 × Age of daughter



=> ( 4x + 10 ) = 3( x + 10 )

=> 4x + 10 = 3x + 30

=> 4x - 3x = 30 - 10

=> x = 20





$\textbf{Hence, Present \: age \: of \: daughter = x \: years = 20 \: years }\\ \textbf{Present \: age \: of \: father = \: 4x = 4( 20 ) = 80 \: years}$

Answer 2

Hola Mate!!

Your answer :-

$let \: the \: present \: age \: of \: daughter = x \\ present \: age \: of \: father = 4x \\ \\ after \: 10 \: years \\ age \: of \: daughter = x + 10 \\ age \: of \: father = 4x + 10 \\ age \: of \: father \: after \: 10 \: years = 3 \: times \: of \: his \: daughter.s \: age \\ \\ hence \: your \: eqution \: becomes = > \\ \\ = 3(x + 10) = 4x + 10 \\ \\ = 3x + 30 = 4x + 10 \\ \\ = 3x - 4x = 10 - 30 \\ \\ = - 1x = - 20 \\ \\ = x = 20 \\ \\ present \: age \: of \: daughter = x = 20 \: years \\ present \: age \: of \: father = 4x = 4 \times 20 = 80 \: years$

☆ Hope it helps ☆