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.



❌spam ❌​

Answer 1

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 :-

Sum of present ages

Solution :-

Six years ago

A - 6/B - 6 = 1/3

3(A - 6) = 1(B - 6)

3A - 18 = B - 6

3A - B = 18 - 6

3A - B = 12 (1)

Now

A + 6/B + 6 = 2/3

3(A + 6) = 2(B + 6)

3A + 18 = 2B + 12

3A - 2B = 12 - 18

3A - 2B = -6

Subtract both

B = 18

Using 1

3a - 18 = 12

3a = 30

a = 30/3

a = 10

Sum = 18 + 10 = 28 years

Answer 2

$\pmb{\bf{\underline{Corrected~ Question~:}}}$

➩ 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 .

$\pmb{\bf{\underline{ Answer ~:}}}$

Given ➩

Ratios of the present age of A & B = 1:3

Ratios of their ages after six years = 2:3

To find ➩

Sum of Present age of A & B = !?

Assume That ➩

Present age of A = x Years

Present age of B = 3x Years

Now ,

→ Their ages after 6 Years

Age of A = 6 + x Years

Age of B = 6 + 3x Years

A/C To Question ➾

• The sums of ratio of their ages (after 6 years) 2:3

$⟹ \: \: \: \: \frac{x + 6}{3x + 6} = \frac{2}{3} \\ \\ ⟹ \: \: \: \: \: \: \: 3(x + 6) = 2(3x + 6) \\ \\ ⟹ \: \: \: \: 3x + 18 = 6x + 12 \\ \\ ⟹ \: \: \: 3x - 6x = 12 - 18 \\ \\⟹ \: \: \: \: - 3x = - 6 \\ \\ ⟹ \: \: \: {\sf{~~\cancel{ - }3x = \cancel{ - }6}} \\ \\ ⟹ \: \: \: x = \frac{6}{3} \\ \\ ⟹ \: \: \: x = \: 2$

The value of x = 2

Now,

Substitute the value of ' x= 2 ' in assumed age of A & B

Age of A = x = 2 years

Age of B = 3x = 3×2 = 6 years

The sum of age of A & B :

$\boxed{\sf\green{2~ + 6~ = ~8years}}$

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