After a joint start, one finishes the remainder: Ajay can do a work in 25 days and Sanjay in 20 days. They work together for 5 days, after which Ajay leaves. In how many days will Sanjay finish the remaining work alone?

Introduction / Context:
Joint work first reduces the remaining fraction, then a single worker completes the rest at his own rate. Track fractions carefully.

Given Data / Assumptions:

• Ajay = 1/25 per day; Sanjay = 1/20 per day.
• First 5 days: both work together.

Concept / Approach:
Compute work done in the first 5 days, subtract from 1, then divide the remainder by Sanjay’s rate.

Step-by-Step Solution:
Combined rate = 1/25 + 1/20 = 9/100 per day.Work in 5 days = 5 * 9/100 = 45/100 = 9/20.Remaining = 1 − 9/20 = 11/20.Sanjay’s rate = 1/20 ⇒ time = (11/20) / (1/20) = 11 days.

Verification / Alternative check:
Translate to 100-unit job: first 5 days produce 45 units; 55 remain; Sanjay at 5 units/day ⇒ 11 days.

Why Other Options Are Wrong:
9, 10, 12, 14 days misrepresent either the first 5-day output or Sanjay’s finishing rate.

Common Pitfalls:
Using averages of times instead of rates; arithmetic slips with fractions.

Final Answer:
11 days