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# Father 's age is three times the sum of the ages of his two children. After 5 years his age will be twice the sum of the ages of two children. Find the age of the father.

Last updated date: 17th Jul 2024
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Hint: Here, we proceed by assuming the father's age is x year and the sum of the children's ages is y, and then solving the question to find the value of x and y.

Complete step by step solution:
Let the age of father =x years
The sum of the age of 2 children =y years
According to the first condition,
The age of the father is thrice the sum of age of his two children.
⇒ x=3y.....let it equation (1)
After 5 years
⇒Father 's age =x+5
⇒The sum of the ages of his two children =y+10 (Here we add 10 because y is the sum of
the age of two children so we add 5 in both the children so it becomes 10).
According to the second condition,
The age of a father became twice the sum of the age of his two children.
⇒x+5=2(y+10)
⇒x+5=2y+20
⇒x−2y=15 ……let it be equation (2)
Put the value of x from equation 1
⇒3y−2y=15
⇒y=15
Put y=15 in equation 1.
⇒x=3×15
⇒x=45
∴The father's age, denoted by x, is 45 years, and the sum of his children's ages, denoted by y, is 15 years.

Note: When faced with such a question on age problems, we always assume the current age in some variables and then apply the conditions of the question on that variable to find out the value of that variable to find out the result.