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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?

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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


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1 answers

1 vote
Answered by on | Votes 1 |

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

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