Question

Six years before, the ages of Salma and Sabir were in the 1 : 2. Six years from now the ratio of their ages will be 3 : 4. Find their present ages.

Answer 1

Solution :-

Let,

Present age of Salma = x

Present age of Sabir = y

Six years before,

Age of Salma = x - 6

Age of Sabir = y - 6

After six years,

Age of Salma = x + 6

Age of Sabir = y + 6

According to the first condition,

$\longrightarrow \sf \dfrac{x-6}{y-6}= \dfrac{1}{2} \\\\\longrightarrow 2(x-6)= y-6 \\\\\longrightarrow 2x-12 = y - 6 \\\\\longrightarrow 2x-y = 6 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...................(1)$

According to the second condition.

$\longrightarrow \sf \dfrac{x+6}{y+6}= \dfrac{3}{4} \\\\\longrightarrow 4(x+6) = 3(y+6) \\\\\longrightarrow 4x+24= 3y+18 \\\\\longrightarrow 4x-3y= -6 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...................(2)$

Multiply eq (1) by 2,

$\longrightarrow\sf 4x-2y = 12 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...................(3)$

Eq (3) - Eq (2),

$\longrightarrow \bf y = 18$

Substitute the value of y in eq (1),

$\longrightarrow \sf 2x - 18 = 6 \\\\\longrightarrow 2x = 24\\\\\longrightarrow \bf x = 12$

Present age of Salma = 12 years

Present age of Sabir = 18 years