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10 years ago, the sum of the ages of two brothers was equal to 1/3rd of the age of father. Elder brother is 2 years older than the younger. At present, sum of their ages is less than the age of father by 14 years. What are the ages of the brothers?

10 years ago, the sum of the ages of two brothers was equal to 1/3rd of the age of father. Elder brother is 2 years older than the younger. At present, sum of their ages is less than the age of father by 14 years. What are the ages of the brothers? Correct Answer 15 and 17

Let age of father, elder son and younger brother be x, y and z respectively

⇒ y – 10 + z – 10 = 1/3(x – 10)

⇒ 3y – 30 + 3z – 30 = x – 10

⇒ –x + 3y + 3z = 50       ---(1)

Given, y – z = 2 ---(2)

Given, x – (y + z) = 14

⇒ x – y – z = 14       ---(3)

On multiplying equation 3 by 3 and adding to 1

⇒ 3x – 3y – 3z – x + y + z = 42 + 50

⇒ 2x = 92

⇒ x = 92/2 = 46

Put x = 46 in 3

⇒ 46 – y – z = 14

⇒ y + z = 32       ---(4)

Adding 2 and 4

⇒ 2y = 34

⇒ y = 17

put y = 17 in 4

⇒ z = 32 – 17 = 15

∴ Ages of brothers are 15 and 17

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