To solve this problem, we need to establish the relationship between the father's and the son's ages over time. Let's break it down step-by-step:
- Let the current age of the son be x years. Therefore, the father's current age is y years.
- According to the problem, 7 years ago, the father's age was 13 years more than twice the son's age. This translates to the equation:
y - 7 = 2(x - 7) + 13 - Expand and simplify the equation:
y - 7 = 2x - 14 + 13
y - 7 = 2x - 1
y = 2x + 6 - Now, we need to find out after how many years the father will be twice as old as the son. We are searching for n, where:
y + n = 2(x + n) - Replace y with the expression we found earlier:
2x + 6 + n = 2(x + n) - Expand the equation:
2x + 6 + n = 2x + 2n - Simplify the equation to solve for n:
6 + n = 2n
6 = n
Therefore, after 6 years, the father's age will be twice the son's age. The correct answer is 6.
Important Questions from Age
- Five times the present age of P exceeds the present age of Q by 29 years. After 8 years, five times Q's age will be 17 years less than seven times P's age at that time. What is the present age (in years) of Q?
If 2 times the mother's age is 26 years more than 4 times her daughter's age, and 3 times the daughter's age is 7 years less than the mother's age, then what is the difference (in years) between the ages of the mother and the daughter?
If 2 times a son's age is added to his father's age, the sum is 36 years. If 2.5 times the father's age is added to the son's age, the sum is 72 years. What is the father's age (in years)?
- Six times the present age of P exceeds the present age of Q by 11 years. After 10 years, three times Q's age will be 27 years less than six times P's age at that time. What is the present age (in years) of Q?
Two times the present age of P exceeds the present age of Q by 41 years. After 7 years, nine times Q's age will be 24 years less than six times P's age at that time. What is the present age (in years) of Q?
