The average age of a Husband and his wife is 39 years. Six years ago, the ratio between their ages was 6 ∶ 5. What is the difference between the present ages of the husband and his wife?
1). 12 years
2). 6 years
3). 3 years
4). 4 years
Let,
Present ages of husband and wife are x years and y years respectively.
? Average of their ages = 39
∴ x + y = 2 × 39
⇒ x + y = 78
⇒ x = 78 – y----- (1)
Six years ago, the ratio between their ages was 6 ? 5
(x – 6) / (y – 6) = 6 : 5
⇒ 5x – 30 = 6y – 36
Put the value of x from Equation (1)
⇒ 5(78 – y) – 30 = 6y – 36
⇒ 390 – 5y – 30 = 6y – 36
⇒ 11y = 360 + 36
⇒ y = 36
Putting this value in (1)
x = 78 – 36 = 42
∴ Required difference between their ages = 42 years – 36 years = 6 years