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A father's age is seven times that of his son's age. Three years from now, the age of the father will be five times that of his son's age. After how many years will their combined age be 58 years?
5 years
6 years
4 years
2 years
5 years
Use the ratio difference: current ratio is 7:1, future ratio is 5:1. Since 3 years pass for both, we solve 7x+3=5(x+3), giving 2x=12, so x=6. Son is 6, Father is 42.
Father's age = 7 * son's age. Three years later, father's age = 5 * (son's age + 3). Combined age target = 58 years.
F=7S, F+3=5(S+3)
Use the ratio difference: current ratio is 7:1, future ratio is 5:1. Since 3 years pass for both, we solve 7x+3=5(x+3), giving 2x=12, so x=6. Son is 6, Father is 42.
Confusing the 'After how many years' question with the current ages of the father and son.
Define ages and solve for current age
Let son's age be x, then father's age is 7x. Three years later, the son is (x+3) and the father is (7x+3). Given 7x+3=5(x+3).
7x+3=5x+15тЯ╣2x=12тЯ╣x=6
Calculate current ages
Son's current age x=6 years. Father's current age 7x=7├Ч6=42 years.
S=6,F=42
Calculate required years for target sum
Let y be the years required. Combined age: (6+y)+(42+y)=58.
48+2y=58тЯ╣2y=10тЯ╣y=5
A is correct because the son is 6 and the father is 42, so in 5 years they will be 11 and 47, which sum to 58.
Age problems are essentially linear system problems; always convert 'times' relations into algebraic equations immediately.
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