Question

The ages of Latha and Sudha are in the ratio 5:6. Eight years from now the ratio of their ages will be 7:8. Find their present ages.

Answer 1

SOLUTION :-

Let,

Present age of Latha = x

Present age of Sudha = y

After 8 years,

Age of Latha = x + 8

Age of Sudha = y + 8

According to the first condition,

$\longrightarrow\sf \dfrac{x}{y} = \dfrac{5}{6} \\\\\longrightarrow x = \dfrac{5}{6}y \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ....................(1)$

According to the second condition,

$\longrightarrow \sf \dfrac{x+8}{y+8}= \dfrac{7}{8} \\\\\longrightarrow 8(x+8) = 7(y+8) \\\\\longrightarrow 8x+64 = 7y + 56 \\\\\longrightarrow 8x-7y = 56-64\\\\\longrightarrow 8x-7y = -8 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ....................(2)$

Substitute the value of x in eq (2),

$\longrightarrow\sf8 \times \dfrac{5}{6}y=7y = -8 \\\\\longrightarrow \dfrac{40y}{6}-7y= -8 \\\\\longrightarrow \dfrac{40y-42y}{6} = -8 \\\\\longrightarrow 40y-42y = -48\\\\\longrightarrow -2y = -48 \\\\\longrightarrow \bf y = 24$

Substitute y = 24 in eq (1),

$\longrightarrow\sf x = \dfrac{5}{6} \times 24 \\\\\longrightarrow x = 5\times 4\\\\\longrightarrow \bf x = 20$

Present age of Latha = 20 years

Present age of Sudha = 24 years