The ratio of the age of a man and his wife is 4 : 3. After 4 years, th

1.	The ratio of the age 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 ?(a) 12 years (b) 8 years (c) 10 years (d) 15 years
Answer» (a) 12 years Let the man’s age = 4x years. Then, Wife’s age = 3x years Given, \(\frac{4x+9}{3x+4}=\frac97\) ⇒ 28x + 28 = 27x + 36 ⇒ x = 8 ∴ Man’s age = 32 years, wife’s age = 24 years Suppose they were married x years ago. Then, \(\frac{32-x}{24-x}=\frac53\) ⇒ 96 – 3x = 120 – 5x ⇒ 2x = 24 ⇒ x = 12

The ratio of the age 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 ?(a) 12 years (b) 8 years (c) 10 years (d) 15 years

Answer»

(a) 12 years

Let the man’s age = 4x years.

Then, Wife’s age = 3x years

Given, \(\frac{4x+9}{3x+4}=\frac97\)

⇒ 28x + 28 = 27x + 36 ⇒ x = 8

∴ Man’s age = 32 years, wife’s age = 24 years

Suppose they were married x years ago.

Then, \(\frac{32-x}{24-x}=\frac53\)

⇒ 96 – 3x = 120 – 5x ⇒ 2x = 24 ⇒ x = 12