Correct Answer: 12

Solution : The ratio of the present ages of a man and his wife = 4 : 3
So, the man's present age = 4a years, and his wife's present age = 3a years
After four years, man's age = (4a + 4) years, and his wife's age = (3a + 4) years
The ratio of the ages after 4 years = 9 : 7
Now, on comparing the ratio with the exact age value,
⇒ $\frac{4a + 4}{3a + 4} = \frac{9}{7}$
⇒ 7(4a + 4) = 9(3a + 4)
⇒ 28a + 28 = 27a + 36
⇒ 28a – 27a = 36 – 28
⇒ a = 8
So, the man's present age = 32 years, and his wife's age = 24 years

Let they were married y years back.
So, y years ago, the man's age = (32 – y) years, his wife's age = (24 – y) years
From the question,
⇒ $\frac{32 – y}{24 – y} = \frac{5}{3}$
⇒ 3(32 – y}) = 5(24 – y)
⇒ 96 – 3y = 120 – 5y
⇒ 5y – 3y = 120 – 96
⇒ 2y = 24
⇒ y = 12

So, they were married 12 years ago. Hence, the first option is correct.