Ages of Lalu and Balu are in the ratio of 1 : 2, after 7 years their ages ratio changes to 3 : 5. The elder person age is:
28
Understanding the Ages Ratio Problem
The question involves finding the current age of the elder person, given the initial ratio of ages and the ratio after a certain number of years. We are told the ages of Lalu and Balu are initially in the ratio 1:2 and after 7 years, their ages are in the ratio 3:5.
Setting Up Initial Ages
Let the current age of Lalu be represented by \(x\) years. Since the ratio of Lalu's age to Balu's age is 1:2, Balu's current age must be \(2x\) years.
- Lalu's current age: \(x\)
- Balu's current age: \(2x\)
Based on the ratio 1:2, Balu is the elder person.
Ages After 7 Years
After 7 years, both Lalu and Balu will be 7 years older. So, their ages will be:
- Lalu's age after 7 years: \(x + 7\)
- Balu's age after 7 years: \(2x + 7\)
Setting Up and Solving the Equation
We are given that after 7 years, their ages are in the ratio 3:5. This can be written as an equation:
\(\frac{x + 7}{2x + 7} = \frac{3}{5}\)
To solve for \(x\), we can cross-multiply:
\(5 \times (x + 7) = 3 \times (2x + 7)\)
Distribute the numbers on both sides:
\(5x + 35 = 6x + 21\)
Now, we need to isolate \(x\). Subtract \(5x\) from both sides:
\(35 = 6x - 5x + 21\)
\(35 = x + 21\)
Subtract 21 from both sides to find the value of \(x\):
\(35 - 21 = x\)
\(14 = x\)
So, the value of \(x\) is 14.
Calculating Current Ages
Using the value of \(x = 14\), we can find the current ages:
- Lalu's current age: \(x = 14\) years
- Balu's current age: \(2x = 2 \times 14 = 28\) years
Let's check the ages after 7 years:
- Lalu's age after 7 years: \(14 + 7 = 21\) years
- Balu's age after 7 years: \(28 + 7 = 35\) years
The ratio of their ages after 7 years is 21:35, which simplifies to \(21/35 = (3 \times 7) / (5 \times 7) = 3/5\). This matches the given ratio, confirming our value of \(x\) is correct.
Finding the Elder Person's Age
The current ages are Lalu: 14 years and Balu: 28 years. The elder person is Balu, and his current age is 28 years.
| Current Age | Age After 7 Years | |
| Lalu | \(x\) | \(x + 7\) |
| Balu | \(2x\) | \(2x + 7\) |
| Ratio | 1:2 | 3:5 |
Substituting \(x=14\):
| Current Age | Age After 7 Years | |
| Lalu | 14 | \(14 + 7 = 21\) |
| Balu | 28 | \(28 + 7 = 35\) |
| Ratio | 14:28 (1:2) | 21:35 (3:5) |
The elder person's age is 28 years.
Revision Table: Ages Ratio Concepts
| Concept | Description | Application in Problem |
| Ratio | A comparison of two quantities. \(a:b = a/b\). | Used to represent the relationship between ages. |
| Algebraic Representation | Using variables to represent unknown quantities. | Let current ages be \(x\) and \(2x\). |
| Equation Formation | Setting up an equality based on the given information. | \(\frac{x + 7}{2x + 7} = \frac{3}{5}\) |
| Solving Linear Equations | Finding the value of the variable. | Cross-multiplication and isolating \(x\). |
Additional Information: Solving Age Ratio Problems
Age-related ratio problems often involve setting up equations based on how ages change over time. Here are key steps:
- Represent Current Ages: Use a variable (like \(x\)) and the given ratio to express the current ages. If the ratio is \(a:b\), ages can be \(ax\) and \(bx\).
- Calculate Ages After/Before Years: Add years for 'after' (\(ax + y\)) or subtract years for 'before' (\(ax - y\)).
- Form the New Ratio Equation: Set the ratio of the modified ages equal to the new given ratio.
- Solve the Equation: Typically involves cross-multiplication and solving a linear equation for the variable.
- Calculate Final Ages: Substitute the value of the variable back into the expressions for the ages to find the required ages.
These problems test your ability to translate word problems into algebraic expressions and solve equations.
Similar Questions
Bipul is 16 years younger than Saibal. 12 years hence, Saibal's age will be 1.5 times that of Bipul. Saibal is now_____years old.
The difference between Charles’ and Shriya’s ages is 6 years. When they married each other 30 years ago, 4 times Cahrle’s age was the same as 5 times the age of Shriya. What is the current sum of their ages?
The difference between Peter and Preeti’s ages is 5 years. When they married each other 35 years ago, 4 times Peter’s age was the same as 5 times the age of Preeti’s. What is the current sum of their ages?
13 years ago, Ram was twice as old as Sunny. Three years from now Sunny’s age will be 3/5 of Ram’s age. What is Ram’s current age?
The ages of X and Y are in the ratio 4 : 7. Three years earlier, the ratio of their ages was 1 : 2. What is the difference between their current ages (Y - X)?
Rathin is now 16 years old while his cousin is 7 years. After how many years will Rathin’s age be 1.5 times that of his cousin?
John is 15 years younger than Jill. 12 years ago, Jill’s age was 1.5 times that of John. Jill is now ______ years old.
Monika’s father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
The present ages of Kavitha, Rajitha and Haritha are in the ratio of 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find the present ages (in years).
Jeremy is 26 years younger than his father. Eight years hence his father’s age will be two years less than twice his age. What is Jeremy’s present age (in years)?
Important Questions from Age
In 2002, Meenu's age was one-third of the age of Meera, whereas in 2010, Meenu's age was half the age of Meera. What is Meenu's year of birth?
A watch loses 2 minutes in every 24 while another watch gains 2 minutes, in 24 hours. At a particular instant, the two watches showed an identical time. Which of the following statements is correct if 24- hour clock is
The sum of the ages of 5 members comprising a family, 3 years ago was 80 years. The average age of the family today is the same as it was 3 years ago, because of an addition of a baby during the intervening period. How old is the baby ?
5 years ago, my sister's age was 5 times my age. Now it is 3 times only. What is my sister's present age (in years)?
The sum of ages of a father and his son is 45 years. Five years ago, the product of their ages (in yrs.) was 124. The present age of father is :
