The present age of the father is twice that of the elder son. Ten years hence the age of the father will be three times that of the younger son. If the difference in ages of the two sons is as 15 years, the present age of the father is:
50 years
To solve this problem, we need to find the present age of the father using the details given in the question. Let's define the variables and understand the information:
- Let the present age of the elder son be \(x\) years.
- Therefore, the present age of the father is \(2x\) years, as the father is twice as old as the elder son.
Ten years hence, the father's age will be \(2x + 10\), and the younger son's age will be \((x - 15) + 10\), as the difference in ages of the two sons is 15 years.
According to the problem, in ten years, the father's age will be three times the age of the younger son. Mathematically, this condition can be written as:
\(2x + 10 = 3[(x - 15) + 10]\)
Simplifying the right side:
- \(x - 15 + 10 = x - 5\)
- \(3(x - 5) = 3x - 15\)
Substituting back, we get:
\(2x + 10 = 3x - 15\)
Solving the equation for \(x\):
- Bring \(3x\) to the left side: \(2x - 3x + 10 = -15\)
- Simplify: \(-x + 10 = -15\)
- Subtract 10 from both sides: \(-x = -25\)
- Therefore, \(x = 25\)
The present age of the father is \(2x = 2 \times 25 = 50\) years.
Therefore, the correct answer is 50 years.
Important Questions from Problem on Age
The ratio of present ages of A and B is 7 : 8. After 6 years from now, the ratio of their ages will be 8 : 9. If C's present age is 10 years more than the present age of A, then the present age (in years) of C is:
Three years ago, the ratio of the age of father to that of his son was 8 ∶ 3. After 4 years, their ages will be in the ratio 11 ∶ 5. What is the present age (in years) of the father?
At present, A is younger than B by 8 years. If 4 years ago, their ages were in the ratio 1 ∶ 2, then what is the present age of B (in years)?
Eight years ago, the ratio of ages of A and B was 5 ∶ 4. The ratio of their present ages is 6 ∶ 5. What will be the sum (in years) of the ages of A and B after 7 years from now?
Ratio of the present age of a mother to that of the daughter is 7 ∶ 1. After 5 years the ratio will become 4 ∶ 1. What is the difference (in years) in their present ages?
