Question

Two years ago, Aryan’s age was seven times the age of Kartik. Eight years hence, the age of Aryan will become twice of the age of Kartik. Find the present age of Aryan.

Please don't use two variables.

Answer 1

$\underline {\blue { At \: present : }}$

$Aryan's \:age = x \: years$

$Karthik's \:age = y \: years$

$\underline {\blue { Two \: years \:ago : }}$

$Aryan's \:age = (x -2)\: years$

$Karthik's \:age = (y -2)\: years$

$\pink { Age \:of \:Aryan = 7( Age \:of \:Kartik)}$

$\implies x - 2 = 7(y-2)$

$\implies x - 2 = 7y - 14$

$\implies x = 7y - 14 +2$

$\implies x = 7y - 12\: --(1)$

$\underline {\blue { After \:8 \: years: }}$

$Aryan's \:age = ( x + 8 )\: years$

$Karthik's \:age = ( y + 8 )\: years$

/* According to the problem */

$x + 8 = 2(y + 8)$

$\implies x + 8 = 2y + 16$

$\implies x = 2y + 16 - 8$

$\implies x = 2y + 8 \:--(2)$

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

$7y - 12 = 2y + 8$

$\implies 7y - 2y = 8 + 12$

$\implies 5y = 20$

$\implies y = \frac{20}{5}$

$\implies y = 4$

/* Substitute y = 4 in equation (1), we get */

$x = 7 \times 4 -12$

$\implies x = 28 - 12$

$\implies x = 16$

Therefore.,

$\red{ Present \:age \: of \;Aryan } \green {= 16 \: years }$

$\red{ Present \:age \: of \: Karthik } \green {= 4 \: years }$

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