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In 10 years, a father will be twice as old as his son. Five years ago, the father was three times as old as his son. Find their current ages.
- a)50 , 20
- b)50 , 10
- c)40 , 12
- d)55 , 12
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
In 10 years, a father will be twice as old as his son. Five years ago,...
- Father's current age = F
- Son's current age = S
Step 1: Translate the first statement into an equation.
F + 10 = 2(S + 10) Simplify: F + 10 = 2S + 20 F = 2S + 10 (Equation 1)
Step 2: Translate the second statement into an equation.
F - 5 = 3(S - 5)
Simplify:
F - 5 = 3S - 15 F = 3S - 10 (Equation 2)
Simplify:
F - 5 = 3S - 15 F = 3S - 10 (Equation 2)
Step 3: Set Equation 1 equal to Equation 2.
2S + 10 = 3S - 10
Subtract 2S from both sides: 10 = S - 10 Add 10 to both sides: S = 20
Subtract 2S from both sides: 10 = S - 10 Add 10 to both sides: S = 20
Step 4: Find Father’s age using Equation 1.
F = 2(20) + 10 F = 50
Answer:
- Father's current age = 50 years
- Son's current age = 20 years
Most Upvoted Answer
In 10 years, a father will be twice as old as his son. Five years ago,...
Understanding the Problem
To solve the problem, we need to set up equations based on the information given about the ages of the father and son.
Step 1: Define Variables
- Let F = Father's current age
- Let S = Son's current age
Step 2: Set Up Equations
1. In 10 years:
- F + 10 = 2(S + 10)
- This implies that in 10 years, the father will be twice as old as his son.
2. Five years ago:
- F - 5 = 3(S - 5)
- This indicates that five years ago, the father was three times as old as his son.
Step 3: Simplify the Equations
From the first equation:
- F + 10 = 2S + 20
- Rearranging gives: F = 2S + 10 - 10
- So, F = 2S + 10
From the second equation:
- F - 5 = 3S - 15
- Rearranging gives: F = 3S - 15 + 5
- So, F = 3S - 10
Step 4: Solve the System of Equations
Now we have two expressions for F:
1. F = 2S + 10
2. F = 3S - 10
Set them equal to each other:
- 2S + 10 = 3S - 10
Rearranging gives:
- 10 + 10 = 3S - 2S
- 20 = S
Now substitute S back to find F:
- F = 2(20) + 10 = 40 + 10 = 50
Conclusion
Thus, the current ages are:
- Father's age = 50 years
- Son's age = 20 years
The correct answer is option 'A': 50, 20.
To solve the problem, we need to set up equations based on the information given about the ages of the father and son.
Step 1: Define Variables
- Let F = Father's current age
- Let S = Son's current age
Step 2: Set Up Equations
1. In 10 years:
- F + 10 = 2(S + 10)
- This implies that in 10 years, the father will be twice as old as his son.
2. Five years ago:
- F - 5 = 3(S - 5)
- This indicates that five years ago, the father was three times as old as his son.
Step 3: Simplify the Equations
From the first equation:
- F + 10 = 2S + 20
- Rearranging gives: F = 2S + 10 - 10
- So, F = 2S + 10
From the second equation:
- F - 5 = 3S - 15
- Rearranging gives: F = 3S - 15 + 5
- So, F = 3S - 10
Step 4: Solve the System of Equations
Now we have two expressions for F:
1. F = 2S + 10
2. F = 3S - 10
Set them equal to each other:
- 2S + 10 = 3S - 10
Rearranging gives:
- 10 + 10 = 3S - 2S
- 20 = S
Now substitute S back to find F:
- F = 2(20) + 10 = 40 + 10 = 50
Conclusion
Thus, the current ages are:
- Father's age = 50 years
- Son's age = 20 years
The correct answer is option 'A': 50, 20.
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