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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 years2). 6 years3). 3 years4). 4 years |
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Answer» 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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