In how many days can 10 women finish the work — which statements suffice? I. 10 men can complete the work in 6 days. II. 10 men and 10 women together complete the work in 3 3/7 days. III. 10 men work for 3 days, and then 10 women finish the remaining.

Question

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

Accepted Answer

Introduction / Context:We must identify which statements suffice to find the time taken by 10 women to finish one unit of work. Treat rates linearly (work/day). Given Data / Assumptions: Let M be the per-man rate; W the per-woman rate. I: 10M completes 1 work in 6 days ⇒ 10M = 1/6. II: (10M + 10W) completes in 3 3/7 days = 24/7 days ⇒ 10M + 10W = 7/24. III: 10M * 3 + 10W * 4 = 1. Concept / Approach:We need 10W (the collective women’s rate) to get time = 1 / (10W). Any two independent equations among I–III determine M and W (or directly 10W). Step-by-Step Solution: I + II ⇒ 10M = 1/6; 10M + 10W = 7/24 ⇒ 10W = 7/24 − 1/6 = 7/24 − 4/24 = 3/24 = 1/8 ⇒ time = 8 days.I + III ⇒ 10M = 1/6 ⇒ work by 10M in 3 days = 1/2; hence 10W * 4 = 1/2 ⇒ 10W = 1/8 ⇒ time = 8 days.II + III ⇒ Solve two equations for M and W; yields the same 10W = 1/8 ⇒ time = 8 days. Verification / Alternative check:Each pair independently leads to 8 days for 10 women. Why Other Options Are Wrong: Listing only specific pairs is too restrictive since multiple pairs suffice. All three together is unnecessary. Common Pitfalls:Adding “days” instead of rates; forgetting to convert 3 3/7 to 24/7 properly. Final Answer:Any two of the three

In how many days can 10 women finish the work — which statements suffice? I. 10 men can complete the work in 6 days. II. 10 men and 10 women together complete the work in 3 3/7 days. III. 10 men work for 3 days, and then 10 women finish the remaining work in 4 days.

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