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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.$$12$$ Years
B.$$8$$ Years
C.$$10$$ Years
D.$$15$$ 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.

Complete step-by-step answer:
Let their present age be $$4x$$ & $$3x$$ .
Then, after $$4$$ years the husband's age $$ = 4x + 4\;$$ and the wife's age $$ = 3x + 4$$ .
So, by the given condition,
  & \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$$ years.
Let their marriage took place P years back.
Then, by the given condition,
  & \dfrac{{32 - p}}{{24 - p}} = \dfrac{5}{3} \cr
  & \Rightarrow 96 - 3p = 120 - 5p \cr
  & \Rightarrow 2p = 24 \cr
  & \Rightarrow p = 12 \cr} $$
Hence, they were married before 12 years i.e. option A

Note: Here ratios were given, all we did is form equations on the basis of conditions were given in question. A ratio may be considered as an ordered pair of numbers, a fraction with the first number in the numerator and the second in the denominator, or as the value denoted by this fraction.