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# The ratio 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?A.$$12$$ YearsB.$$8$$ YearsC.$$10$$ YearsD.$$15$$ years

Last updated date: 20th Jun 2024
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Hint: Ratio of their ages at present time are given as well as ratio of their ages after four years also given, we have to form equations, after that solving equations we will get the answer.

Let their present age be $$4x$$ & $$3x$$ .
Then, after $$4$$ years the husband's age $$= 4x + 4\;$$ and the wife's age $$= 3x + 4$$ .
\eqalign{ & \dfrac{{4x + 4}}{{3x + 4}} = \dfrac{9}{7} \cr & \Rightarrow 28x + 28 = 27x + 36 \cr & \Rightarrow x = 8 \cr}
Then the present age of the husband $$= 4 \times 8years = 32$$ years &
the wife's age $$= 3 \times 8$$ years $$= 24$$ years.
\eqalign{ & \dfrac{{32 - p}}{{24 - p}} = \dfrac{5}{3} \cr & \Rightarrow 96 - 3p = 120 - 5p \cr & \Rightarrow 2p = 24 \cr & \Rightarrow p = 12 \cr}