Meenu is 38 years old. Her daughter is 8 years old. In how many years will Meenu be double her daughter's age?
22
Solving Meenu and Daughter Age Word Problem
This problem is a classic example of an age-based word problem that can be solved using linear equations. We are given the current ages of Meenu and her daughter and asked to find the number of years after which Meenu's age will be exactly double her daughter's age.
Setting Up the Age Problem
Let's define the current ages:
- Meenu's current age = 38 years
- Daughter's current age = 8 years
We want to find the number of years from now when Meenu's age will be double her daughter's age. Let 'x' be the number of years we are looking for.
After 'x' years:
- Meenu's age will be \(38 + x\) years
- Daughter's age will be \(8 + x\) years
The problem states that after 'x' years, Meenu's age will be double her daughter's age. We can write this as an equation:
\(\text{Meenu's age after x years} = 2 \times (\text{Daughter's age after x years})\)
\(38 + x = 2 \times (8 + x)\)
Solving the Equation for the Number of Years
Now, we need to solve the linear equation for 'x':
\(38 + x = 2(8 + x)\)
First, distribute the 2 on the right side of the equation:
\(38 + x = 16 + 2x\)
Next, we want to isolate 'x' on one side of the equation. We can subtract 'x' from both sides:
\(38 + x - x = 16 + 2x - x\)
\(38 = 16 + x\)
Now, subtract 16 from both sides to find the value of 'x':
\(38 - 16 = 16 + x - 16\)
\(22 = x\)
So, after 22 years, Meenu will be double her daughter's age.
Verification of the Solution
Let's check if this answer is correct by calculating their ages after 22 years:
- Meenu's age after 22 years = \(38 + 22 = 60\) years
- Daughter's age after 22 years = \(8 + 22 = 30\) years
Is Meenu's age double her daughter's age? \(60 = 2 \times 30\). Yes, \(60 = 60\). The condition is satisfied.
Therefore, in 22 years, Meenu will be double her daughter's age.
| Age | Current | After 22 Years |
|---|---|---|
| Meenu | 38 | 38 + 22 = 60 |
| Daughter | 8 | 8 + 22 = 30 |
The number of years required is 22.
Revision Table: Key Concepts in Age Problems
| Concept | Explanation | How it applies here |
|---|---|---|
| Representing Unknowns | Use variables (like \(x\)) for the quantities you need to find (e.g., number of years, age). | We used \(x\) for the number of years. |
| Expressing Future/Past Ages | To find age after \(y\) years, add \(y\) to current age. To find age \(y\) years ago, subtract \(y\). | We used \(38 + x\) and \(8 + x\) for future ages. |
| Forming Equations | Translate the relationships given in the problem into algebraic equations. | "Meenu's age will be double her daughter's age" translates to \(38 + x = 2(8 + x)\). |
| Solving Linear Equations | Use algebraic techniques (distribute, combine like terms, isolate the variable) to find the value of the unknown. | We solved \(38 + x = 16 + 2x\) to get \(x = 22\). |
Additional Information: Types of Age Problems
Age problems often involve relationships between the ages of two or more people at different points in time. Common types include:
- Finding ages after/before a certain number of years: Similar to this problem.
- Problems involving sums or differences of ages: "The sum of their ages is X", "A is Y years older than B".
- Problems involving ratios of ages: "The ratio of their ages is A:B".
- Problems involving products of ages: Less common, but possible.
The key to solving these problems is carefully defining variables and translating the given information into algebraic equations.
Similar Questions
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Important Questions from Problem on Age
The ratio of present ages of Neelam and Rajni is 6 : 7. After four years, their ages will be in the ratio of 8 : 9. What is the present age of Rajni?
Five years ago the age of the son was one third of that of his mother at that time. If the sum of their present ages is 70 years, then find the present age of the mother.
Jaya is 36 years old and her son Bharat is 11 years old. In how many years will Jaya be twice as Bharat's age?
The ratio of a father's age to his son's age is 3 ∶ 2 The product of the numbers representing their age is 486. The ratio of their ages after 5 years will be:
X said to Y, "At the time of your birth I was twice as old as you are at present." If the present age of X is 42 years, then consider the following statements:
1. 8 years ago, the age of X was five times the age of Y.
2. After 14 years, the age of X would be two times the age of Y.
Which of the above statements is/are correct?
