A alone can finish a job in 24 days, and B alone in 16 days. Working together with C, they finish the job in 8 days. In how many days can C alone finish the job?

Introduction / Context:This is a standard rate extraction problem: use individual times for A and B and the joint time for all three to isolate the third individual rate.

Given Data / Assumptions:

• A: 24 days ⇒ rate 1/24 per day.
• B: 16 days ⇒ rate 1/16 per day.
• A + B + C: 8 days ⇒ rate 1/8 per day.

Concept / Approach:Sum A and B rates, subtract from the combined rate to get C’s rate, then invert to get C’s time.

Step-by-Step Solution:

Verification / Alternative check:Check: 1/24 + 1/16 + 1/48 = 2/48 + 3/48 + 1/48 = 6/48 = 1/8, consistent with the given joint time.

Why Other Options Are Wrong:32, 36, 40, 24 do not match the extracted rate from the combined data and lead to incorrect total rates when recombined.

Common Pitfalls:Arithmetic mistakes with denominators 24, 16, and 8; forgetting to subtract A + B from the total rather than averaging times.

Final Answer:48 days