Workers A, B, and C can complete a job at different individual times. A alone takes 10 days; B alone takes 24 days. When A, B, and C work together, they finish the job in 6 days. In how many days can C alone complete the job?

Introduction / Context:
Given individual completion times for A and B, and the combined time for A+B+C, we find C's solo time by subtracting known rates from the combined rate. This is a standard rate decomposition problem.

Given Data / Assumptions:

• A's time = 10 days ⇒ rate = 1/10 job/day.
• B's time = 24 days ⇒ rate = 1/24 job/day.
• (A+B+C) time = 6 days ⇒ combined rate = 1/6 job/day.

Concept / Approach:
Let rC be C's rate. Then rC = 1/6 - (1/10 + 1/24). Convert to a single fraction and then invert to get C's required days (1/rC).

Step-by-Step Solution:

Verification / Alternative check:
Check: 1/10 + 1/24 + 1/40 = 12/120 + 5/120 + 3/120 = 20/120 = 1/6. Valid.

Why Other Options Are Wrong:
25, 50, 75, 60 do not satisfy the exact rate balance when combined with A and B to produce 1/6 job/day.

Common Pitfalls:
Arithmetic slips when summing fractions or inverting the final rate; not using a common denominator can lead to errors. Keep precise fractions to avoid rounding mistakes.

Final Answer:
40