A can complete a work in 20 days and B in 30 days. A works alone for 4 days, after which B and C together complete the remaining work in 18 days. In how many days can C alone complete the entire work?

Introduction / Context:
We first deduct the portion done by A, then use the joint duration of B and C to solve for C's rate. Finally, invert to get C's solo time.

Given Data / Assumptions:

• A = 1/20 per day; B = 1/30 per day.
• A works 4 days → work done = 4/20 = 1/5.
• Remaining work = 4/5 completed by (B + C) in 18 days.

Concept / Approach:
(B + C) rate = remaining work / time. Subtract B's rate to get C's rate; then invert for time.

Step-by-Step Solution:

Verification / Alternative check:
Back-substitute: In 18 days, B does 18*(1/30)=3/5; C does 18*(1/90)=1/5; total 4/5 → consistent.

Why Other Options Are Wrong:
Do not match the derived C rate; misinterpretation of the staged work often leads to wrong values like 72 or 84.

Common Pitfalls:
Forgetting to subtract A's initial contribution; mixing up rates and times when combining workers.

Final Answer:
90