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

Answer:

28

Explanation:

compare both ratios from that we find one part vale is 4 years, then we substitute in any one ratio to get the present ages.

Answer 2

Given : Six years ago the ratio of ages of A & B was 1:3 & After six years the ratio will be 2:3.

To Find : Find the sum of present ages of A and B ?

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Solution : Let the age of A & B six years be x and 3x.

$~$

• Present age of A = x + 6
• Present age of B = 3x + 6
• $\leadsto$After 6 years

$~$

◗Age of A = x + 6 + 6 = x + 12 years

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

$~$

$\qquad{\sf:\implies{x~+~\dfrac{12}{3x}~+~12~\dfrac{2}{3}}}$

$\qquad{\sf:\implies{3\bigg(x~+~12\bigg)~=~2\bigg(3x~+~12\bigg)}}$

$\qquad{\sf:\implies{3x~+~36~=~6x~+~24}}$

$\qquad{\sf:\implies{3x~-~6x~=~24~-~36}}$

$\qquad{\sf:\implies{- 3x~=~- 12}}$

$\qquad{\sf:\implies{x~=~\dfrac{- 12}{- 3}}}$

$\qquad{\sf:\implies{x~=~\cancel\dfrac{12}{3}}}$

$\qquad:\implies{\underline{\boxed{\frak{\purple{x~=~4}}}}}$★

$~$

• Present age of A = x + 6 = 10 years
• Present age of B = 3x + 6 = 3(4) + 6 = 18 years

$~$

◗Sum of ages = 10 + 18

$~$

Hence,

$\therefore\underline{\sf{The~ sum ~of ~present ~ages ~of ~A~\&~ B~is~\bf{\underline{28~years}}}}$