Question

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

Answer 1

♣ Given :-

• Six years ago the ratio of ages of A & B was 1:3

• After six years the ratio will be 2:3.

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♣ To Calculate :-

• Sum of present ages of A and B.

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♣ Solution :-

Let,

• Present age of A be = x years

• Present age of B be = y years

《 Six years ago 》

• Age of A = (x - 6) years

• Age of B = (y - 6) years

According to the Given Condition:

$\bf \frac{x - 6}{y - 6} = \frac{1}{3} \\ \\ :\longmapsto\sf3(x - 6) = y - 6 \\ \\ :\longmapsto \sf 3x - 18 = y - 6 \\ \\ :\longmapsto \bf 3x - y = 12 \: \: \: \: .\: . \: .\: \{i \}$

《 After Six years 》

• Age of A = (x + 6) years

• Age of B = (y + 6) years

According to the Given Condition :

$\bf\frac{x + 6}{y + 6} = \frac{2}{3} \\ \\ :\longmapsto \sf 3(x + 6) = 2(y + 6) \\ \\ :\longmapsto \sf 3x + 18 = 2y + 12 \\ \\ :\longmapsto \bf3x - 2y = - 6 \: \: \: \:. \: . \: . \: \{ii \}$

Subtracting {ii} from {i}

$\purple{ \Large :\longmapsto  \underline {\boxed{{\bf y = 18} }}}$

Putting Value of y in {i} We get,

$\sf3x = 12 + 18 \\ \\ :\longmapsto \sf3x = 30 \\ \\\purple{ \Large :\longmapsto  \underline {\boxed{{\bf x = 10} }}}$

Hence ,

• Present age of A = 10 years

• Present age of B = 18 years

So,

$\bf Sum \: of \: Present \: Ages \\ \bf of \: A \: and \: B = 10 + 18 \\ \\ \Large\purple{:\longmapsto{\pmb{ \underline{\boxed{ \text{S}um =28 \: years}}}}}$

$\LARGE\red{\mathfrak{  \text{W}hich \:\:is\:\: the\:\: required} }\\ \Huge \red{\mathfrak{ \text{ A}nswer.}}$

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Answer 2

Given :-

Six years ago the ratio of ages of A&B was 1:3 and after six years the ratio becomes 2:3

To Find :-

Present ages

Solution :-

Let the age of A and B six years ago be x and 3x

Present age of A = x + 6

Present age of B = 3x + 6

After 6 years

Age of A = x + 6 + 6 = x + 12 years

Age of B = 3x + 6 + 6 = 3x + 12 years

x + 12/3x + 12 = 2/3

3(x + 12) = 2(3x + 12)

3x + 36 = 6x + 24

3x - 6x = 24 - 36

-3x = -12

x = -12/-3

x = 12/3

x = 4

Therefore

Present age of A = x + 6 = 10 years

Present age of B = 3x + 6 = 3(4) + 6 = 18 years

Now,

Sum of ages = 10 + 18

Sum of ages = 28 years