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?

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:

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