Question

Q. The ratio between the ages of a man and his wife is 4:3. After 4 years, this ratio will be 9:7. If at the time of marriage, the ratio was 5:3, then how many years ago were they married?

Answer 1

let the age of man presently be x, and of wife is y

so
$\frac{x}{y } = \frac{4}{3}$
so 3x=4y
so
$x = \frac{4}{3} y$

after 4 years,
$\frac{x + 4}{y + 4} = \frac{9}{7}$
so 7(x+4)=9(y+4)
7x+28=9y+36

so 7x-9y=8
put x=4y/3

we get y=24. thus x=32



at marriage,
let the years of marriage be 'a'

so
$\frac{32 - a}{24 - a} = \frac{5}{3}$

thus we get a=12


thus they were married 12 years ago

Answer 2

Given:

• The ratio of the ages of a man and his wife is 4:3
• After 4 years, the ratio will be 9:7
• Time of marriage, the ratio was 5:3

To find:

• Years ago they married?

Solution:

✪ Lets consider the Present age of man and his wife be 4x and 3x respectively.

Then, After 4 years,⠀⠀⠀⠀

• Husband's age = (4x + 4) years
• Wife's age = (3x + 4) years

$\begin{gathered}\underline{\boldsymbol{ \textsf{ \textbf{According\:to \:the \:given \:Condition,}}}}\\\end{gathered}$

• After 4 years, The ratio of the age of a man and his wife will be 9:7.⠀⠀⠀⠀⠀

$\begin{gathered}:\implies\sf \dfrac{4x + 4}{3x + 4} = \dfrac{9}{7}\\\\\\ :\implies\sf 7(4x + 4) = 9(3x + 4)\\\\\\ :\implies\sf 28x + 28 = 27x + 36\\\\\\ :\implies\sf 28x - 27x = 36 - 28\\\\\\ :\implies{\underline{\boxed{\frak{{x = 8}}}}}\blue\bigstar\\\\\end{gathered}$

Therefore,

• The Present age of Man, 4x = 4×8 = 32 years
• The Present age of his wife, 3x = 3×8= 24years

✪ Now, Lets assume that their marriage took place in "T years" back.

⠀⠀⠀⠀

Then, By given Condition,

• The ratio of the age of a man and his wife at the time of marriage is 5:3.

$\begin{gathered}:\implies\sf \dfrac{32 - T}{24 - T} = \dfrac{5}{3}\\\\\\ :\implies\sf 3(32 - T) = 5(24 - T)\\\\\\ :\implies\sf 96 - 3T = 120 - 5T\\\\\\ :\implies\sf 5T - 3T = 120 - 96\\\\\\:\implies\sf 2T = 24\\\\\\:\implies\sf T = \cancel{\dfrac{24}{2}}\\\\\\ :\implies{\underline{\boxed{\frak{{T = 12\:years}}}}}\pink\bigstar\\\\\end{gathered} \\ \\ \therefore\:{\underline{\sf{Hence,{They\:were\:married}\:\pmb{12\:years}\:\sf{ago}.}}}$

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||TheUnknownStar||