Question

Theas of Rina and Riyan are in the ratio 3:5. Four years from now the ratio of
es will be 5:7. Find their present ages.​

Answer 1

SOLUTION :-

Let,

Present age of Rina = x

Present age of Riyan = y

After 4 years,

Age of Rina = x + 4

Age of Riyan = y + 4

According to the first condition,

$\longrightarrow \sf \dfrac{x}{y}= \dfrac{3}{5} \\\\\longrightarrow \sf x=\dfrac{3}{5} y \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .....................(1)$

According to the second condition,

$\longrightarrow\sf \dfrac{x+4}{y+4}=\dfrac{5}{7} \\\\\longrightarrow 7(x+4)= 5(y+4) \\\\\longrightarrow 7x+28= 5y+20 \\\\\longrightarrow 7x-5y= -8 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .....................(2)$

Substitute the value of x in equation (2),

$\longrightarrow \sf 7\times \left(\dfrac{3}{5} y \right)- 5y= -8 \\\\\longrightarrow \dfrac{21y}{5}-5y = - 8 \\\\\longrightarrow \dfrac{21y-(5y\times 5)}{5}= -8 \\\\\longrightarrow \dfrac{21y-25y}{5}= - 8 \\\\\longrightarrow \dfrac{-4y}{5} = -8 \\\\\longrightarrow -4y = -40 \\\\\longrightarrow \bf y= 10$

Substitute y = 10 in equation (1),

$\longrightarrow\sf x = \dfrac{3}{5}y \\\\\longrightarrow x = \dfrac{3}{5}\times 10 \\\\\longrightarrow x = 3\times2\\\\\longrightarrow \bf x = 6$

Present age of Rina = 6 years

Present age of Riyan = 10 years