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: Problem Identification:
This is an age-related word problem solvable with a system of linear equations.

Step 2: Formulation of Equations:
Let F represent the father's current age and S represent the son's current age.
The problem statements translate to the following 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 in 10 years: F + 10
Son's age in 10 years: S + 10
$\implies (F + 10) = (S + 10) + 30$

Step 3: Solution Derivation:
The system of equations is:
(1) $F = 2S + 4$
(2) $F + 10 = S + 40 \implies F = S + 30$

Equating the expressions for F:
$2S + 4 = S + 30$
Subtracting S from both sides:
$S + 4 = 30$
Subtracting 4 from both sides:
$S = 26$
The son's current age is 26 years.

Substituting S=26 into equation (2) to find F:
$F = 26 + 30 = 56$

Verification with equation (1):
$F = 2(26) + 4 = 52 + 4 = 56$
The father's current age is 56 years.

Step 4: Conclusion:
The father's present age is 56 years.