The ratio of the present ages of Asha and Lata is 5 : 6. If the difference between their ages is 6 years, then what will be Lata’s age after 5 years?
41
Solving Age Ratio Problems: Finding Future Age
This problem involves finding the future age of a person based on the ratio of present ages and the difference between them. We are given the ratio of the present ages of Asha and Lata and the difference in their ages. We need to calculate Lata's age after 5 years.
Let's break down the problem and solve it step-by-step.
Understanding the Age Ratio
The present ages of Asha and Lata are in the ratio 5 : 6. This means that for some common multiplier, let's call it \(x\), Asha's age is \(5x\) years and Lata's age is \(6x\) years.
- Asha's present age = \(5x\) years
- Lata's present age = \(6x\) years
Since the ratio is 5:6, Lata is currently older than Asha. The difference in their ages is given as 6 years.
Using the Age Difference to Find the Multiplier
The difference between their ages is the difference between the larger age (Lata's) and the smaller age (Asha's).
Difference in ages = Lata's present age - Asha's present age
We are given this difference is 6 years.
So, we can set up the equation:
\(6x - 5x = 6\)
Now, we solve for \(x\):
\(x = 6\)
The common multiplier \(x\) is 6.
Calculating Present Ages
Now that we know the value of \(x\), we can find the present ages of Asha and Lata:
- Asha's present age = \(5x = 5 \times 6 = 30\) years
- Lata's present age = \(6x = 6 \times 6 = 36\) years
We can quickly check the difference: \(36 - 30 = 6\), which matches the information given in the problem.
Calculating Lata's Age After 5 Years
The question asks for Lata's age after 5 years. To find this, we add 5 years to Lata's present age.
Lata's age after 5 years = Lata's present age + 5 years
Lata's age after 5 years = \(36 + 5 = 41\) years
Summary of Calculations
| Step | Description | Calculation | Result |
|---|---|---|---|
| 1 | Represent ages using ratio | Asha: \(5x\), Lata: \(6x\) | Asha: \(5x\), Lata: \(6x\) |
| 2 | Set up equation from difference | \(6x - 5x = 6\) | \(x = 6\) |
| 3 | Calculate present ages | Asha: \(5 \times 6\), Lata: \(6 \times 6\) | Asha: 30, Lata: 36 |
| 4 | Calculate Lata's age after 5 years | \(36 + 5\) | 41 |
Therefore, Lata's age after 5 years will be 41 years.
Revision Table: Key Concepts
| Concept | Explanation |
|---|---|
| Ratio of Ages | Represents the proportional relationship between the ages of two or more people at a specific point in time. If the ratio is \(a:b\), ages can be represented as \(ax\) and \(bx\). |
| Age Difference | The difference in age between two people remains constant throughout their lives. If the difference is \(D\) and ages are \(ax\) and \(bx\) (\(b > a\)), then \(bx - ax = D\). |
| Future Age | To find someone's age after \(N\) years, add \(N\) to their present age. Present age + \(N\) years = Future age. |
Additional Information: Solving Age Problems
Age-related problems often involve ratios, sums, or differences of ages at different points in time (past, present, or future). Here are some common types and approaches:
- Age Sum Problems: If the sum of ages is given, say \(S\), and the ratio is \(a:b\), then \(ax + bx = S\). Solve for \(x\) and find the ages.
- Problems with Past/Future Ages: If the ratio or sum is given for a past time (say, \(Y\) years ago) or a future time (say, \(Z\) years from now), adjust the present ages accordingly before setting up the equation.
- Age \(Y\) years ago = Present age - \(Y\)
- Age \(Z\) years from now = Present age + \(Z\)
- Using one variable: Sometimes, if the difference is given directly (e.g., A is 6 years older than B), you can represent ages as \(B\) and \(B+6\) without using a ratio multiplier initially, depending on the problem structure.
Always carefully read whether the given information (ratio, sum, difference) refers to present ages, past ages, or future ages.
Important Questions from Quant Based Puzzle
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