Question

Six years before the ages of salma and Sanitation were in the ratio 1:2six years from now the ratio of their ages will be 3:4.find their present ages.

Answer 1

Given:

• Six years before ratio of ages of Salma & Sanitation = 1:2.

• Six years from now ratio of their ages of Salma & Sanitation = 3:4.

To Find:

• Present ages of Salma & Sanitation.

Solution:

☯ Let the present ages of Salma & Sanitation be x and y.

$\sf\underline{\bigstar\;Case \: 1:}$

$:\implies\sf{ \frac{x - 6}{y - 6} = \frac{1}{2} } \\ \\ :\implies\sf{2x - 12 = y - 6} \\ \\ :\implies\sf{2x - y = - 6 + 12} \\ \\ :\implies\sf{2x - y = 6} \\ \\ :\implies\sf{ - y = 6 - 2y} \\ \\ :\implies{\boxed{\sf{\red{y = 2x - 6 \: .... \: (1)}}}} \: \bigstar$

$\sf\underline{\bigstar\;Case \: 2:}$

$:\implies\sf{ \frac{x + 6}{y + 6} = \frac{3}{4} } \\ \\ :\implies\sf{4x + 2y = 3y + 18} \\ \\ :\implies\sf{4x - 3y = 18 - 24} \\ \\ :\implies\sf{4x - 3y = - 6} \\ \\ :\implies\sf{4x - 3(2x - 6) = - 6 \: .... \: (From \: 1)} \\ \\ :\implies\sf{4x - 6x + 18 = - 6} \\ \\ :\implies\sf{ - 2x = - 6 - 18} \\ \\ :\implies\sf{ - 2x = - 24} \\ \\ :\implies{\boxed{\sf{\red{x = 12}}}} \: \bigstar$

Thus,

$\star \: \sf{Age \: of \: Salma = 12 \: years.}$

$\star \: \sf{Age \: of \: Sanitation \: y = 2x - 6} \\ \\ :\implies\sf{y = 2 \times (12) - 6} \\ \\ :\implies\sf{y = 24 - 6} \\ \\ :\implies\sf{y = 18}$

Thus,

• Present ages of Salma & Sanitation are 12 & 18 years.

Answer 2

$\large \rm \color{aqua} { Age \: of \: Salma \: = x=12years}$

$\large \rm \color{cyan} { Age \: of \: Sanitation \: = y=18years}$

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