Priyanshu is three time as old as his brother .five year later, he wil

1.	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» ong> 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

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»

ong>

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