A brother is elder than his sister by 5 years . If you add 6 to the fifth part of the brother's age and 5 to the third part of the sister's age the result is same. Find their ages.
Solve the sum by taking the age of brother as x+5 and sister age as x.
Answers
Answer:
☛Hence, Age of elder brother is 20 years and age of his sister is 15 years.
Step-by-step explanation:
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.
Step-by-step explanation:
Assume that the age of sister be x years and brother be y years.
A brother is elder than his sister by 5 years.
→ y = x + 5 .............(1)
If you add 6 to the fifth part of the brother's age and 5 to the third part of the sister's age the result is same.
As per given condition,
→ y/5 + 6 = x/3 + 5
→ (y + 30)/5 = (x + 15)/3
→ 3y + 90 = 5x + 75
→ 3(x + 5) + 90 = 5x + 75
→ 3x + 15 + 90 = 5x + 75
→ 3x + 105 = 5x + 75
→ 2x = 30
→ x = 15
Substitute value of x in (1)
→ y = 15 + 5
→ y = 20
Hence, the age of brother is 20 years and sister is 15 years.