Question

The present age of a father is 4 years more than double the age of his son. After 10 years, the father's age is 30 years more than his son. Then the present age of father is:

• A. 26 years
• B. 28 years
• C. 56 years
• D. 60 years

Hint:

Always define your variables clearly (e.g., F = father's \textbf{present} age). When dealing with future or past ages, remember to add or subtract the time from the present age for \textbf{both} individuals.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This is a word problem involving ages that can be solved by setting up a system of linear equations.
Step 2: Key Formula or Approach:
Let F be the present age of the father and S be the present age of the son.
Translate the given statements into two equations.
1. "The present age of a father is 4 years more than double the age of his son." \(\implies F = 2S + 4\)
2. "After 10 years, the father's age is 30 years more than his son."
Father's age after 10 years = F + 10
Son's age after 10 years = S + 10
\(\implies (F + 10) = (S + 10) + 30\)
Step 3: Detailed Explanation:
We have two equations:
(1) \(F = 2S + 4\)
(2) \(F + 10 = S + 40 \implies F = S + 30\)
Now we can solve this system. Since both equations are equal to F, we can set them equal to each other:
\(2S + 4 = S + 30\)
Subtract S from both sides:
\(S + 4 = 30\)
Subtract 4 from both sides:
\(S = 26\)
The son's present age is 26 years.
Now, find the father's present age using either equation. Let's use equation (2):
\(F = S + 30 = 26 + 30 = 56\)
Let's verify with equation (1):
\(F = 2S + 4 = 2(26) + 4 = 52 + 4 = 56\)
Both equations give the same result. The father's present age is 56 years.
Step 4: Final Answer:
The present age of the father is 56 years.