Repairing a partially broken stem: infer Z’s daily percentage X can do 20% of the work per day, Y can do 25% of the work per day, and together X, Y, and Z can do 50% of the work per day. What percentage of the work per day is done by Z alone?

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

Accepted Answer

Introduction / Context:This question asks for Z’s solo percentage contribution when daily percentages for X and Y are known, and a combined daily percentage for X+Y+Z is given. The original stem had missing words; we apply recovery to make it solvable without altering the core intent. Given Data / Assumptions: X does 20% of the job per day ⇒ 0.20 per day. Y does 25% per day ⇒ 0.25 per day. Together X+Y+Z do 50% per day ⇒ 0.50 per day. Concept / Approach:Percentages per day add for independent workers. Thus, Z’s rate is (X+Y+Z) − (X+Y). Step-by-Step Solution: Rate(X) = 0.20Rate(Y) = 0.25Rate(X+Y+Z) = 0.50Therefore, Rate(Z) = 0.50 − (0.20 + 0.25) = 0.05 = 5% Verification / Alternative check:0.20 + 0.25 + 0.05 = 0.50, which matches the combined daily percentage. Why Other Options Are Wrong:10%, 15%, 20% overstate Z’s share given the fixed total of 50%. Common Pitfalls:Confusing percentage of work with fraction of the day; here percentages are per-day work fractions. Final Answer:5%

Repairing a partially broken stem: infer Z’s daily percentage X can do 20% of the work per day, Y can do 25% of the work per day, and together X, Y, and Z can do 50% of the work per day. What percentage of the work per day is done by Z alone?

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