Question : Directions: The ratio of the ages of a man and his wife is 4 : 3. After 4 years, the ratio will be 9 : 7. If at the time of marriage, the ratio was 5 : 3, how many years ago were they married?
Option 1: 12
Option 2: 24
Option 3: 5
Option 4: 8
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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.
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