Question

father's age is 3 times the sum of his two children age after 5 years his his age will be twice the sum of the age of 2 children find the age of the father

Answer 1

age of father=15 years

Answer 2

Hello mate!!

Let me help!

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$ANSWER:$

Let Father's age be x

Let sum of ages of children be y

After 5 years,

Father's age will be x + 5

and sum of ages of children will be y + 5

Solution:

As father's age is 3 times the sum of ages of his children,

x = 3y

x - 3y = 0 — [1]

As father's age will be twice the sum of his two children,

x + 5 = 2 (y + 10) [ as it is sum of ages of 2 children, we take y + 10 instead of y + 5]

x + 5 = 2y + 20

x - 2y = 15 — [2]

Multiply eq [1] by 2 and eq [2] by 3,

2x - 6y = 0 —[3]

3x - 6y = 45 —[4]

Subtracting eq [3] from [4],

therefore, x = 45

Substituting x = 45 in eq [1]

45 - 3y = 0

-3y = -45

-y = -15

therefore, y = 15

For father's age,

x = 3y

x = 3 × 15

x = 45

therefore, Father's age = 45 years.

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Hope this helps!