Question

A brother is elder than his sister by 5 years if you add 6 to fifth part of brother's age and 5 to the third part of sister's age the result is same. Find their ages . ​

Answer 1

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Answer 2

Let the age of brother and sister be x and y respectively.

According to the question,

☛ Brother is elder than his sister by 5 years.

or

➜ x = 5 + y

➜ y = x - 5 -----(i)

Also,

☛ if you add 6 to fifth part of brother's age and 5 to the third part of sister's age the result is same.

or

➜ x/5 + 6 = 5 + y/3

➜ x + 30 / 5 = 15 + y / 3

➜ 3x + 90 = 75 + 5y

➜ 3x - 5y = -15 ------(ii)

From (i) , y = x - 5

Substituting y = x - 5 in eq.(ii)

➜ 3x - 5y = -15

➜ 3x - 5 ( x - 5 ) = -15

➜ 3x - 5x + 25 = -15

➜ 2x = 40

➜ x = 40/2

➜ x = 20

Substituting x = 20 in eq(i),

☛ y = x - 5

➜ y = 20 - 5

➜ y = 15

Hence, Age of elder brother is 20 years and age of his sister is 15 years.