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

Let the present age of man = $$4x$$ years and wife = $$3x$$ years

According to ques,

=> $$\frac{4x+4}{3x+4}=\frac{9}{7}$$

=> $$28x+28=27x+36$$

=> $$28x-27x=36-28$$

=> $$x=8$$

Thus, man's age = $$4\times8=32$$ years and his wife's age = $$24$$ years

Let they were married $$x$$ years ago, then ratio at the time of marriage = 5 : 3

=> $$\frac{32-x}{24-x}=\frac{5}{3}$$

=> $$96-3x=120-5x$$

=> $$5x-3x=120-96$$

=> $$2x=24$$

=> $$x=\frac{24}{2}=12$$ years

=> Ans - (A)