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Tom’s father is thrice as old as Tom. 10 years ago, Tom’s father’s age was 7 times his age. What is Tom’s current age?
- a)14 years
- b)15 years
- c)16 years
- d)17 years
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Tom’s father is thrice as old as Tom. 10 years ago, Tom’s ...
Let Tom’s age and his father age be A and B years respectively.
Tom’s father is thrice as old as Tom,
⇒ B = 3A
10 years ago, Tom’s father’s age was 7 times his age,
⇒ (B – 10) = 7(A – 10)
⇒ A = 15
∴ Tom's age is 15 years.
Most Upvoted Answer
Tom’s father is thrice as old as Tom. 10 years ago, Tom’s ...
Understanding the Problem
To solve the problem, we need to define the ages of Tom and his father in terms of variables. Let's denote:
- Tom's current age as T
- Tom's father's current age as F
According to the problem, we have two key pieces of information:
1. Age Relationship
- Tom's father is thrice as old as Tom:
- F = 3T
2. Age Difference from the Past
- Ten years ago, Tom's father was 7 times Tom's age:
- F - 10 = 7(T - 10)
Setting Up the Equations
Now, we can substitute F from the first equation into the second:
- 3T - 10 = 7(T - 10)
Solving the Equation
1. Expand the equation:
- 3T - 10 = 7T - 70
2. Rearrange to isolate T:
- 3T - 7T = -70 + 10
- -4T = -60
- T = 15
Conclusion
Thus, Tom's current age is 15 years.
Verification
Let's verify our solution:
- If Tom is 15, then Tom's father is:
- F = 3 * 15 = 45 years old.
- Ten years ago:
- Tom was 5 years old (15 - 10).
- His father was 35 years old (45 - 10).
- Check the ratio:
- 35 = 7 * 5, confirming that 10 years ago, the father's age was 7 times Tom's age.
Thus, the correct answer is option 'B': Tom is currently 15 years old.
To solve the problem, we need to define the ages of Tom and his father in terms of variables. Let's denote:
- Tom's current age as T
- Tom's father's current age as F
According to the problem, we have two key pieces of information:
1. Age Relationship
- Tom's father is thrice as old as Tom:
- F = 3T
2. Age Difference from the Past
- Ten years ago, Tom's father was 7 times Tom's age:
- F - 10 = 7(T - 10)
Setting Up the Equations
Now, we can substitute F from the first equation into the second:
- 3T - 10 = 7(T - 10)
Solving the Equation
1. Expand the equation:
- 3T - 10 = 7T - 70
2. Rearrange to isolate T:
- 3T - 7T = -70 + 10
- -4T = -60
- T = 15
Conclusion
Thus, Tom's current age is 15 years.
Verification
Let's verify our solution:
- If Tom is 15, then Tom's father is:
- F = 3 * 15 = 45 years old.
- Ten years ago:
- Tom was 5 years old (15 - 10).
- His father was 35 years old (45 - 10).
- Check the ratio:
- 35 = 7 * 5, confirming that 10 years ago, the father's age was 7 times Tom's age.
Thus, the correct answer is option 'B': Tom is currently 15 years old.
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Tom’s father is thrice as old as Tom. 10 years ago, Tom’s father’s age was 7 times his age. What is Tom’s current age?a)14 yearsb)15 yearsc)16 yearsd)17 yearsCorrect answer is option 'B'. Can you explain this answer?
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