Asha is 25% more efficient than Usha. Usha takes 25 days to complete a piece of work alone. Asha starts the work alone; Usha joins her exactly 5 days before completion. For how many days did Asha work alone?

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

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Introduction / Context:Efficiency is inversely proportional to time. If Usha’s time is known, Asha’s rate can be derived from the 25% efficiency increase. Then split the timeline into Asha-alone and together phases. Given Data / Assumptions: Usha time = 25 days ⇒ rate u = 1/25 job/day. Asha is 25% more efficient ⇒ rate a = 1.25 * u = 1/20. Usha joins 5 days before completion. Concept / Approach:Let total duration be T days. Then Asha works alone for (T − 5) days and with Usha for the last 5 days. Sum of completed fractions equals 1 job. Step-by-Step Solution: Asha-alone work = (T − 5) * (1/20).Together work (last 5 days) = 5 * (1/20 + 1/25) = 5 * (9/100) = 45/100 = 9/20.Equation: (T − 5)/20 + 9/20 = 1 ⇒ (T − 5 + 9)/20 = 1 ⇒ (T + 4)/20 = 1 ⇒ T = 16.Asha-alone days = T − 5 = 11. Verification / Alternative check:Check totals: 11*(1/20) + 5*(9/100) = 11/20 + 9/20 = 1; consistent. Why Other Options Are Wrong:9/10/12/15 do not satisfy the exact work-balance equation. Common Pitfalls:Applying 25% to time instead of rate; forgetting the last 5 days are combined work. Final Answer:11

Asha is 25% more efficient than Usha. Usha takes 25 days to complete a piece of work alone. Asha starts the work alone; Usha joins her exactly 5 days before completion. For how many days did Asha work alone?

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