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.

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

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: H = 2S − 4.S * (2S − 4) = 240 ⇒ 2S^2 − 4S − 240 = 0.Divide by 2: S^2 − 2S − 120 = 0.Factor: (S − 12)(S + 10) = 0 ⇒ S = 12 (reject −10).Therefore Seema’s age = 12 years. Verification / Alternative check: H = 2*12 − 4 = 20; product 20*12 = 240 ✓ and 2S = 24 = H + 4 = 24 ✓ 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

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.

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