Question

five years ago arman uncle was three times are old as arman ten years from now his uncle Will be twice as old as arman what are the present ages of arman and his uncle ​

Answer 1

Solution :-

Let :-

Present age of Arman = x

Present age of Arman's uncle = y

Five years ago :-

Age of Arman = x - 5

Age of Arman's uncle = y - 5

After 10 years :-

Age of Arman = x + 10

Age of Arman's uncle = y + 10

According to the first condition :-

$\longrightarrow \sf 3(x-5) = y - 5 \\\\\longrightarrow 3x-15 = y - 5 \\\\\longrightarrow 3x-y = 10 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .................(1)$

According to the second condition :-

$\longrightarrow \sf 2(x+10)= y + 10 \\\\\longrightarrow 2x+20 = y + 10 \\\\\longrightarrow 2x-y = - 10 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .................(2)$

Equation (1) - Equation (2) :-

$\bf \longrightarrow x = 20$

Substitute the value of x in eq(1) :-

$\longrightarrow \sf 3 \times 20 - y = 10 \\\\\longrightarrow -y = 10 -60\\\\\longrightarrow -y = -50 \\\\\longrightarrow \bf y = 50$

Present age of Arman = 20 years

Present age of Arman's uncle = 50 years

Answer 2

Required Answer:

let aman's uncle current age = a

arlmaan's current age be = b

According to question..

$\sf \: (a - 5) = 3 \times (b - 5)$

$\sf \: a = 3b - 10 \rightarrow(1)$

10 years later,

$\sf \: (a + 10) = 2(b + 10)$

$\sf \: a = 2b + 10 \rightarrow(2)$

From equation (1) and (2),

$\sf \:(1) - (2)$

$\bold {b = 20}$

Substitute $\bold {b = 20}$ in equation (1)

$\sf\: a = 3\times \:20 - 10$

$\sf\:a = 60 - 10$

$\bold{a = 50}$