The ratio of the age of a gentleman and his wife is 4 : 3. After 4 years this…
2025
The ratio of the age of a gentleman and his wife is 4 : 3. After 4 years this ratio will be 9 : 7. If at the time of their marriage the ratio was 5 : 3, how many years ago they were married?
- A.
10 years
- B.
8 years
- C.
12 years
- D.
15 years
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Correct answer: C
Solution: Let the present ages of the gentleman and his wife be 4x and 3x respectively.
After 4 years the ratio becomes (4x + 4) : (3x + 4) = 9 : 7.
Solve: 7(4x + 4) = 9(3x + 4) ⇒ 28x + 28 = 27x + 36 ⇒ x = 8.
So present ages are 4x = 32 and 3x = 24.
Let y be the number of years ago they were married. Then (32 - y) : (24 - y) = 5 : 3.
Solve: 3(32 - y) = 5(24 - y) ⇒ 96 - 3y = 120 - 5y ⇒ 2y = 24 ⇒ y = 12.
Therefore they were married 12 years ago.
Check: 12 years ago their ages were 20 and 12, which gives the ratio 20:12 = 5:3 as required.
Answer: 12 years