Finding an Individual's Time from a Trio's Combined Time A can do the work in 24 days, B in 30 days, and together with C they finish in 12 days. How long would C take to complete the work alone?

Introduction / Context:
We are given two individual times and a combined time with a third worker. Convert to rates and solve for C's rate by subtraction, then invert to get C's solo time.

Given Data / Assumptions:

• A: 24 days ⇒ 1/24 per day.
• B: 30 days ⇒ 1/30 per day.
• A + B + C: 12 days ⇒ 1/12 per day.

Concept / Approach:
r_C = r_total − (r_A + r_B). Then time_C = 1/r_C.

Step-by-Step Solution:
r_A + r_B = 1/24 + 1/30 = (5 + 4)/120 = 9/120 = 3/40.r_total = 1/12 = 10/120.r_C = 10/120 − 9/120 = 1/120.C alone time = 1 / (1/120) = 120 days.

Verification / Alternative check:
Rates add up: 1/24 + 1/30 + 1/120 = 1/12, confirming consistency.

Why Other Options Are Wrong:
100, 125, 72, or 90 days do not match the rate difference result.

Common Pitfalls:
Arithmetic slips when adding fractions; always use a common denominator.

Final Answer:
120 days