Question

=RHS.
Example 19: Present ages of Anu and Raj are in the ratio 4:5. Eight years from now
the ratio of their ages will be 5:6. Find their present ages.​

Answer 1

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Answer 2

SOLUTION :-

Let,

Present age of Anu = x

Present age of Raj = y

After 8 years,

Age of Anu = x + 8

Age of Raj = y + 8

According to the first condition,

$\longrightarrow\sf \dfrac{x}{y}=\dfrac{4}{5} \\\\\longrightarrow x= \dfrac{4}{5}y \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .................(1)$

According to the second condition,

$\longrightarrow\sf \dfrac{x+8}{y+8}=\dfrac{5}{6}\\\\\longrightarrow 6(x+8)= 5(y+8) \\\\\longrightarrow 6x+48 = 5y+40\\\\\longrightarrow 6x-5y=-8 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .................(2)$

Substitute the value of x in eq(2),

$\longrightarrow\sf 6\times \dfrac{4}{5}y+5y= -8 \\\\\longrightarrow \dfrac{24y}{5}+5y= -8 \\\\\longrightarrow \dfrac{24y-25y}{5}=-8\\\\\longrightarrow -y = -40 \\\\\longrightarrow\bf y = 40$

Substitute y = 40 in eq (1),

$\longrightarrow\sf x= \dfrac{4}{5}\times 40 \\\\\longrightarrow x= 4 \times 8 \\\\\longrightarrow\bf x = 32$

Present age of Anu = 32 years

Present age of Raj = 40 years