Question

The present ratio of ages of A&B was 1:3 and after six years are ratio becomes 2:3.find the sum of present age of A&B. IP​

Answer 1

Answer :-

• The sum of the present ages of A and B is 8 years.

To find :-

• The sum of the present ages of A and B.

Solution :-

• The present ages of A and B are in the ratio 1 : 3.

Let :-

• A's present age be "x" years.
• B's present age be "3x" years.

After 6 years :-

• A's age will be "x + 6" years.
• B's age will be "3x + 6" years.

It is given that :-

• After 6 years, the ratio of the ages of A and B becomes 2 : 3.

Therefore,

$\underline{\boxed{\bf x + 6 : 3x + 6 = 2 : 3}}$

$\dashrightarrow \rm \dfrac{x + 6}{3x + 6} = \dfrac{2}{3}$

$\rm \dashrightarrow 3 \: (x + 6) =2 \: (3x + 6)$

$\rm \dashrightarrow 3x + 18 = 6x + 12$

$\rm \dashrightarrow 3x - 6x = 12 - 18$

$\rm \dashrightarrow -3x = -6$

$\rm \dashrightarrow x = \dfrac{-6}{-3}$

$\rm \dashrightarrow x = 2$

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Hence,

$\sf A's \: present \: age = x = 2 \: years.$

$\sf B's \: present \: age = 3x = 3 \times 2 = 6 \: years.$

And :-

$\sf Sum \: of \: their \: ages = 2 + 6 = 8 \: years.$

Answer 2

★ Required Answer ,

• The sum of the ages of A and B is 8 years

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★ Given that ,

• The present ratio of ages of A&B are 1:3
• after six years the ratio becomes 2:3

★ To Find ,

• The sum of present ages of A and B

★ Assumptions ,

• Let the present age of A be x
• Let the Present age of B be 3x

✪ Their ages after six years will be,

• A's age after 6 years will be x + 6
• B's age after 6 years will be 3x + 6

★ According to the question ,

• The ratio of their ages after 6 years will become 2 : 3

★ Framing an equation we get ,

$:\implies \bf x + 6 : 3x + 6 = 2 : 3$

$:\implies \bf \dfrac{x+6}{3x + 6 } = \dfrac{2}{3}$

✪ Cross Multiplying the equation :

$:\implies \bf 3(x + 6)= 2(3x + 6 )$

$:\implies \bf 3x + 18 = 6x + 12$

$:\implies \bf 18 - 12 = 6x - 3x$

$:\implies \bf 6 = 3x$

✪ Solving the equation in  further :

$:\implies \bf 3x = 6$

$:\implies \bf x = \cancel\dfrac{6}{2}$

$:\implies {\pink{\underline{\boxed{\frak{ x = 2 }}}\bigstar}}$

★ Now let's find their ages ,

$:\implies {\red{\bf {A's \; age\; will \;be = x = 2 years}}}$

$:\implies {\purple{\bf {B's \; age\; will \;be = 3x = 6 years }}}$

★Therefore ,

• The sum of their present ages will be 8 years

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