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?

Difficulty: Easy

5%
10%
15%
20%
None of these

Correct Answer: 5%

Explanation:

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.

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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