The ratio of the ages of a man and his wife i | vedclass

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Question

(C) Let the present ages of the man and his wife be $4x$ and $3x$ respectively.After $4$ years,their ages will be $(4x + 4)$ and $(3x + 4)$.According

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(C) Let the present ages of the man and his wife be $4x$ and $3x$ respectively.After $4$ years,their ages will be $(4x + 4)$ and $(3x + 4)$.According to the problem,the ratio after $4$ years is $9:7$:$\frac{4x + 4}{3x + 4} = \frac{9}{7}$$7(4x + 4) = 9(3x + 4)$$28x + 28 = 27x + 36$$x = 8$So,the present ages are: Man $= 4(8) = 32$ years,Wife $= 3(8) = 24$ years.Let them have been married $y$ years ago. At that time,their ages were $(32 - y)$ and $(24 - y)$.The ratio at the time of marriage was $5:3$:$\frac{32 - y}{24 - y} = \frac{5}{3}$$3(32 - y) = 5(24 - y)$$96 - 3y = 120 - 5y$$2y = 24$$y = 12$Therefore,they were married $12$ years ago.

The ratio of 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?

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