Question

Three years ago, Gautam was thrice as old as
his sister Reena. After three years Gautam will
be twice as old as Reena. What is the present
age of Reena?​

Answer 1

$Let \: present \:age \:of \:Reena = x \: years$

$Let \: present \:age \:of \: Gautam = y\: years$

$\underline{\pink{ 3 \: years \: ago : }}$

$Age \: of \: Reena = ( x - 3 ) \: years$

$Age \:of \: Gautam = ( y - 3 ) \: years$

/* According to the problem given */

$y - 3 = 3(x-3)$

$\implies y = 3x - 9 + 3$

$\implies y = 3x - 6\ : ---(1)$

$\underline{\pink{ After \:3 \: years : }}$

$Age \: of \: Reena = ( x + 3 ) \: years$

$Age \:of \: Gautam = ( y + 3 ) \: years$

/* According to the problem given */

$y+3 = 2( x+3)$

$\implies y = 2x + 6 - 3$

$\implies y = 2x + 3 \: ---(2)$

/* From (1) and (2), we get */

$3x - 6 = 2x + 3$

$\implies 3x - 2x = 3 + 6$

$\implies x = 9$

Therefore.,

$\red{ Present \:age \:of \: Reena } \green { = 9 \:years }$

•••♪