Rajeev is 4 years older than Shilpa. Shilpa's present age can be obtained by subtracting four times her age 4 years ago from four times her age 4 years from now. What was Rajeev's age 4 years ago?

Introduction / Context:
This puzzle uses an unusual wording to define Shilpa's present age from her past and future ages. We also know that Rajeev is 4 years older than Shilpa. Translating the description into algebra provides a neat way to compute both their ages and the required past age of Rajeev.

Given Data / Assumptions:

• Rajeev is 4 years older than Shilpa at present.
• Shilpa's present age equals four times her age 4 years from now minus four times her age 4 years ago.
• We must find Rajeev's age 4 years ago.
• All ages are in whole years and time flows uniformly.

Concept / Approach:
Let Shilpa's present age be S years. Then her age 4 years from now is S + 4, and 4 years ago it was S - 4. The statement says S = 4(S + 4) - 4(S - 4). We solve this equation for S. Then Rajeev's present age is S + 4, and his age 4 years ago is (S + 4) - 4.

Step-by-Step Solution:
Let Shilpa's present age be S years. Her age 4 years from now will be S + 4. Her age 4 years ago was S - 4. Given that S = 4(S + 4) - 4(S - 4). Compute the right side: 4(S + 4) = 4S + 16 and 4(S - 4) = 4S - 16. So S = (4S + 16) - (4S - 16) = 4S + 16 - 4S + 16 = 32. Therefore Shilpa's present age S is 32 years. Rajeev is 4 years older, so his present age is 32 + 4 = 36 years. Rajeev's age 4 years ago was 36 - 4 = 32 years.

Verification / Alternative check:
Verify the condition for Shilpa. Four years ago she was 28 and in four years she will be 36. Then 4 times her future age is 4 * 36 = 144, and 4 times her past age is 4 * 28 = 112. The difference 144 - 112 = 32, which equals her present age. Rajeev at 36 is indeed 4 years older, and 4 years ago he was 32, matching our answer.

Why Other Options Are Wrong:
If Rajeev were 36 years old four years ago, his present age would be 40, which changes Shilpa's present age and breaks the relation. Ages 28 or 30 also fail to satisfy the special equation for Shilpa. The option 40 years is similarly inconsistent. Only 32 years as Rajeev's age four years ago fits all given data.

Common Pitfalls:
The unusual sentence structure may cause confusion. Some learners misread it and form S = 4(S - 4) - 4(S + 4) or reverse the subtraction order. Others forget that Rajeev is older and incorrectly add or subtract 4. Carefully writing equalities for ages at each time point avoids these problems.

Final Answer:
Hence, Rajeev was 32 years old four years ago.