Ages — product and linear relation: The product of Harish’s and Seema’s present ages is 240. Also, twice Seema’s age exceeds Harish’s age by 4 years. Find Seema’s present age in years.

Introduction / Context:
Here we mix a multiplicative constraint (product of ages) with a linear relationship. Setting variables and solving a quadratic yields the answer efficiently.

Given Data / Assumptions:

• H * S = 240, where H = Harish, S = Seema.
• 2S is greater than H by 4 ⇒ 2S = H + 4.

Concept / Approach:
Express H in terms of S from the linear relation, substitute into the product, solve for S, and select the positive, realistic root.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 20, 10, 14 years do not satisfy both the product and the linear relation simultaneously.

Common Pitfalls:

• Using H = 2S + 4 instead of H + 4 = 2S.
• Dropping the negative root reasoning; ages cannot be negative.

Final Answer:
12 years