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

Step-by-step explanation:

Let the present age of Salma be x

And present age of Sabir be y

Six years ago:-

Age of Salma = x - 6

Age of Sabir = y - 6

Given, Six years before, the ratio of their ages is 1 : 2

⇢ x - 6 : y - 6 = 1 : 2

⇢ $\rm \dfrac{x-6}{y-6} = \dfrac{1}{2}$

By cross multiplication:-

⇢ 2(x - 6) = 1(y - 6)

⇢ 2x - 12 = y - 6

⇢ 2x - y = - 6 + 12

⇢ 2x - y = 6......(i)

Six years later:-

Age of Salam = x + 6

Age of Sabir = y + 6

Given, Six years later, the ratio of their ages is 3 : 4

⇢ x + 6 : y + 6 = 3 : 4

⇢ $\rm \dfrac{x+6}{y+6} = \dfrac{3}{4}$

By cross multiplication:-

⇢ 4(x + 6) = 3(y + 6)

⇢ 4x + 24 = 3y + 18

⇢ 4x - 3y = -6......(ii)

Multiply equation (i) with 2

⇢ 2( 2x - y = 6)

⇢ 4x - 2y = 12......(iii)

Equation (iii) - (ii)

⇢ 4x - 2y - (4x - 3y) = 12 - (-6)

⇢ 4x - 2y - 4x + 3y = 12 + 6

⇢ y = 18

Substitute y = 18 in equation (i)

⇢ 2x - y = 6

⇢ 2x - 18 = 6

⇢ 2x = 6 + 18 = 24

⇢ x = $\dfrac{24}{2}$ = 12

Therefore:-

⇝ Present age of Salma = x = 12 years

⇝ Present age of Sabir = y = 18 years

Answer 2

$\LARGE{\bf{\underline{\underline{GIVEN:-}}}}$

• Before 6 years, Ages of Salma and Sabir were in the ratio 1:2.
• After 6 years, Ages of Salma and Sabir were in the ratio 3:4.

$\LARGE{\bf{\underline{\underline{TO \ FIND:-}}}}$

• We need to find their present ages.

$\LARGE{\bf{\underline{\underline{SOLUTION:-}}}}$

▣ Let the ages of Salma and Sabir be x and y respectively.

Six years before:

• Age of Salma = x-6.
• Age of Kabir = y-6

Given that ratio of their ages is 1:2. In other words:

$\implies \sf \dfrac{Age \ of \ Salma}{Age \ of \ Kabir} =\dfrac{1}{2}$

$\implies \sf \dfrac{x-6}{y-6} =\dfrac{1}{2}$

Cross multiplying and further solving, we get:

$\implies \sf 2x=y+6$

Six years after:

• Age of Salma = x+6.
• Age of Kabir = y+6

Given that the ratio of their ages is 3:4. In other words:

$\implies \sf \dfrac{Age \ of \ Salma}{Age \ of \ Kabir} =\dfrac{3}{4}$

$\implies \sf \dfrac{x+6}{y+6} =\dfrac{3}{4}$

Cross multiplying and further simplifying, we get:

$\sf \implies4x=3y-6$

∴We get two equations:

$\implies \sf 2x=y+6$

$\sf \implies4x=3y-6$

We can use the elimination method. Multiply "2" to the first equation.

$\implies \sf 2(2x)=2(y+6)$

$\implies \sf 4x=2y+12$

Therefore, we can rewrite our equations:

$\implies \sf 4x=2y+12$

$\sf \implies4x=3y-6$

Subtract these equations. We get:

$\leadsto \sf{\red{y=18}}$

Substitute y=18 in any of the equations.

$\implies \sf 2x=y+6$

$\implies \sf 2x=18+6$

$\implies \sf x=\dfrac{24}{2}$

$\implies \sf x=12$

Therefore, The age of Salma is 12 years and age of sabir is 18 years.