-
The ratio of 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?
-
- 15 years
- 12 years
- 10 years
- 8 years
Correct Option: B
Let the present ages of the man and his wife are 4x and 3x years respectively; then
After 4 years ages of man and his wife will be 4x + 4 and 3x + 4 years.
According to question,
After 4 years, this ratio of their ages will be 9 : 7,
(4x + 4)/ (3x + 4) = 9/7
⇒ (4x + 4)7 = 9(3x + 4)
⇒ 28x + 28 = 27x + 36
∴ x = 8
Hence, their present ages are 4 x 8 = 32 years and 3 x 8 = 24 years
If t years ago they were married, then
(32 - t) /(24 - t) = 5/3
⇒ (32 - t)3 = 5(24 - t)
⇒ 96 -3t = 120 - 5t
⇒ 2t = 24
∴ t = 12 years
