[12 years] The ratio of the age of a man and his wife is 4:3. At the time of marriage the ratio was 5:3 and Aft

For Competitive Exams

The ratio of the age of a man and his wife is 4:3. At the time of marriage the ratio was 5:3 and After 4 years this ratio will become 9:7. How many years ago were they married?

8 years

10 years

11 years

12 years

Explanation:

Let the present age of the man and his wife be 4$x$ and 3$x$ respectively.

After 4 years this ratio will become 9 : 7

=> $\left(4x + 4\right)$ : $\left(3x + 4\right)$ = 9 : 7

=> 7$\left(4x + 4\right)$ = 9$\left(3x + 4\right)$

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

=> $x$ = 8

Present age of the man = 4$x$ = 4×8 = 32

Present age of his wife = 3$x$ = 3×8 = 24

Assume that they got married before t years. Then

(32 - t) : (24 - t) = 5 : 3

3(32 - t) = 5(24 - t)

=> 96 - 3t = 120 - 5t

=> 2t = 24

=> t = $\dfrac{24}{2}$ = 12

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