Question

Priyanshu is three time as old as his brother .five year later, he will be only 5/2 time older than his brother .how old are they now​

Answer 1

SOLUTION :-

Let,

Present age of the brother = x

Present age of Priyanshu = y

Five years later,

Age of the brother = x + 5

Age of Priyanshu = y + 5

According to the first condition,

$\longrightarrow \sf y = 3x \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ......................(1)$

According to the second condition,

$\longrightarrow\sf y+5 =\dfrac{5}{2} \times (x+5) \\\\\longrightarrow 2(y+5)=5(x+5) \\\\\longrightarrow 2y+10 = 5x+25 \\\\\longrightarrow 5x-2y = 10-25 \\\\\longrightarrow 5x-2y = -15 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ......................(2)$

Substitute y = 3x in equation (2),

$\longrightarrow\sf 5x-2 (3x) = -15 \\\\\longrightarrow 5x-6x = -15 \\\\\longrightarrow -x = -15 \\\\\longrightarrow \bf x = 15$

Present age of the brother = 15 years

Present age of Priyanshu = 3 × 15

                                           = 45 years