The ratio of the present ages of Anil and Aakash is 4 : 5. Three years later, the ratio of their ages will be 7 : 8. What is the present age, in years, of Anil?

Introduction / Context:
This problem is a typical age ratio question where the ratio of present ages is given along with the ratio of future ages after a fixed number of years. The task is to determine the actual present age of one person. Such questions test your ability to convert ratio information into algebraic equations and handle time shifts correctly.

Given Data / Assumptions:

• At present, the ages of Anil and Aakash are in the ratio 4 : 5.
• After 3 years, the ratio of their ages will be 7 : 8.
• We must find Anil present age.
• Ages are measured in years and are positive integers.

Concept / Approach:
We express Anil and Aakash present ages in terms of a common multiple using the given ratio. After 3 years, we add 3 to each expression and impose the second ratio as an equation. This leads to an algebraic equation in the common multiple, which we solve to obtain the actual ages. The method illustrates how ratios and linear equations work together in age problems.

Step-by-Step Solution:
Step 1: Let Anil present age be 4x years and Aakash present age be 5x years. Step 2: After 3 years, Anil age will be 4x + 3 years. Step 3: After 3 years, Aakash age will be 5x + 3 years. Step 4: At that time, the ratio of their ages is given as 7 : 8. Step 5: Therefore, (4x + 3) / (5x + 3) = 7 / 8. Step 6: Cross multiply to obtain 8 * (4x + 3) = 7 * (5x + 3). Step 7: Expand both sides: 32x + 24 = 35x + 21. Step 8: Rearrange: 32x - 35x = 21 - 24, so -3x = -3. Step 9: Divide by -3 to get x = 1. Step 10: Therefore, Anil present age is 4x = 4 * 1 = 4 years.

Verification / Alternative check:
With x = 1, Aakash present age is 5 years. After 3 years, their ages will be 4 + 3 = 7 years for Anil and 5 + 3 = 8 years for Aakash. The ratio 7 : 8 exactly matches the condition given in the problem. This confirms that our calculated ages are consistent with both the present and future ratios, and thus the answer is correct.

Why Other Options Are Wrong:
Option A (8 years) would lead to a present ratio that is inconsistent with the ratio 4 : 5 when Aakash age is determined.
Option B (6 years) would not produce the correct ratio of 7 : 8 after 3 years when matched with a suitable age for Aakash.
Option D (10 years) similarly fails to satisfy both ratio conditions simultaneously, so it cannot be the correct answer.

Common Pitfalls:
One common mistake is to apply the ratio 7 : 8 directly to present ages instead of to ages after 3 years. Another error is to forget to add 3 to both ages when forming the future ratio equation. It is also easy to commit algebraic mistakes while cross multiplying and simplifying. Careful step by step writing of expressions is the safest way to avoid such issues.

Final Answer:
The present age of Anil is 4 years.