A man is 41 years old, and his son is 9 years old. In how many years will the father be three times as old as the son?
A. 3 years
B. 5 years
C. 7 years
D. 9 years
Step-by-Step Solution:
To find out how many years it will take for the father to be three times as old as his son, we need to set up a mathematical equation based on their current ages and the future situation.
Let x be the number of years after which the father will be three times as old as his son.
- Father’s current age: 41 years
- Son’s current age: 9 years
In x years, the father’s age will be:
41 + x
In x years, the son’s age will be:
9 + x
We are told that after x years, the father will be three times as old as the son:
41 + x = 3 times (9 + x)
Now, let’s solve this step by step.
Step 1: Expand the equation
The equation is:
41 + x = 3 (9 + x)
First, expand the right-hand side:
41 + x = 27 + 3x
Step 2: Rearrange the equation
Now, let’s move all terms involving x to one side and constants to the other side:
41 – 27 = 3x – x
Simplify:
14 = 2x
Step 3: Solve for x
Now, divide both sides by 2:
x = 14/2 = 7
Conclusion:
After 7 years, the father will be three times as old as his son. Therefore, the correct answer is 7 years.
Verification:
- In 7 years, the father’s age will be: 41 + 7 = 48 years.
- In 7 years, the son’s age will be: 9 + 7 = 16 years.
Checking if the father is three times as old as the son:
48 = 3 \times 16
Yes, 48 is three times 16, so the solution is correct.
Conclusion:
In 7 years, the father will be three times as old as the son, making the correct answer 7 years. This type of age-based word problem is common in competitive exams, and solving it requires setting up an algebraic equation that represents the situation described. By following the steps outlined above, you can easily arrive at the correct answer.