The father of Ramesh is 27 years older than Ramesh. After 5 years, the ratio of their ages will be 2:3. Calculate their present ages.

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Points to Remember:

  • This is a word problem involving ages and ratios.
  • We need to set up algebraic equations to solve for Ramesh’s and his father’s current ages.
  • The solution will involve solving a system of simultaneous equations.

Introduction:

This question is a classic age problem that tests the ability to translate word problems into mathematical equations. Age problems often involve relationships between the ages of different individuals at different points in time. These problems are solved using algebraic techniques, typically involving setting up and solving simultaneous equations. The core concept revolves around understanding the relationship between current ages and future ages.

Body:

Setting up the Equations:

Let’s represent Ramesh’s current age as ‘x’ years. The problem states that his father is 27 years older than Ramesh. Therefore, his father’s current age is ‘x + 27’ years.

After 5 years, Ramesh’s age will be ‘x + 5’ and his father’s age will be ‘(x + 27) + 5 = x + 32’.

The problem further states that the ratio of their ages after 5 years will be 2:3. This can be expressed as the following equation:

(x + 5) / (x + 32) = 2/3

Solving the Equations:

To solve this equation, we cross-multiply:

3(x + 5) = 2(x + 32)

3x + 15 = 2x + 64

3x – 2x = 64 – 15

x = 49

Therefore, Ramesh’s current age (x) is 49 years.

His father’s current age is x + 27 = 49 + 27 = 76 years.

Verification:

After 5 years:

Ramesh’s age: 49 + 5 = 54
Father’s age: 76 + 5 = 81

Ratio of their ages: 54/81 = 2/3 (This confirms our solution)

Conclusion:

In summary, Ramesh’s current age is 49 years, and his father’s current age is 76 years. This solution was obtained by translating the word problem into a system of algebraic equations and solving for the unknown variables. The solution was then verified by checking if the ratio of their ages after 5 years matches the given ratio of 2:3. This problem highlights the importance of careful reading, accurate translation of word problems into mathematical expressions, and the application of basic algebraic techniques to solve real-world problems. The ability to solve such problems demonstrates a fundamental understanding of mathematical reasoning and problem-solving skills.

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