A and B together can complete a work in 12 days; B and C together can complete it in 16 days. A works alone for 5 days; B works alone for 7 days; then C works alone and finishes the job in 13 days. In how many days can C alone complete the entire.

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Solve this multiple-choice question and choose the correct option.

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Introduction / Context:We are given pairwise joint times and a staged completion where each person works alone for specified days. Setting individual daily rates for A, B, C and using the data leads to a solvable linear system. Given Data / Assumptions: a + b = 1/12 (job/day). b + c = 1/16 (job/day). 5 days of A, 7 days of B, and 13 days of C complete the job: 5a + 7b + 13c = 1. Concept / Approach:Solve the system for c. From the first two equations express a and c in terms of b, or use elimination. Once c is known, C’s solo time is 1/c. Step-by-Step Solution: From a + b = 1/12 and b + c = 1/16, solve simultaneously with 5a + 7b + 13c = 1.The unique solution is a = 1/16, b = 1/48, c = 1/24.Therefore, C alone takes 1 / (1/24) = 24 days. Verification / Alternative check:Check sums: a + b = 1/16 + 1/48 = 3/48 + 1/48 = 1/12; b + c = 1/48 + 1/24 = 1/48 + 2/48 = 1/16; and 5a + 7b + 13c = 5/16 + 7/48 + 13/24 = 1 (after common denominator), confirming consistency. Why Other Options Are Wrong:16/32/48/20 days do not match the solved value c = 1/24. Common Pitfalls:Trying to average the given times or mis-adding fractions; always set rate equations first. Final Answer:24 days

A and B together can complete a work in 12 days; B and C together can complete it in 16 days. A works alone for 5 days; B works alone for 7 days; then C works alone and finishes the job in 13 days. In how many days can C alone complete the entire work?

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