Question

Ten years ago mohan was thrice as old as ram was, but 10 years hence he will be only twice as old. find mohan''s present age.

Answer 1

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

$Age \: of \: Mohan = x \: years$

$Age \: of \:Ram = y \: years$

$\underline {\pink { 10 \: years \:ago : }}$

$Age \: of \: Mohan = (x - 10) \: years$

$Age \: of \:Ram = ( y - 10 )\: years$

/* According to the problem given */

$Mohan's \:age = 3 \times ( Ram's \: age )$

$\implies x - 10 = 3(y-10)$

$\implies x = 3y- 30 + 10$

$\implies x = 3y- 20 \: ---(1)$

$\underline {\orange { After \:10 \: years : }}$

$Age \: of \: Mohan = (x + 10) \: years$

$Age \: of \:Ram = ( y + 10 )\: years$

/* According to the problem given */

$Mohan's \:age = 2 \times ( Ram's \: age )$

$\implies x + 10 = 2(y+10)$

$\implies x = 2y+ 20 - 10$

$\implies x = 2y + 10 \: ---(2)$

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

$3y - 20 = 2y + 10$

$\implies 3y - 2y = 20 + 10$

$\implies y = 30$

/* Put y = 30 in equation (1) , we get */

$x = 3 \times 30 - 20$

$\implies x = 90 - 20$

$\implies x = 70$

Therefore.,

$\red { Mohan's \: present \:age } \green {= 70 \: years }$

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