Who is fastest given partial-work times: X can do 1/4 of the work in 10 days, Y can do 40% of the work in 40 days, and Z can do 1/3 of the work in 13 days. If they work individually, who will finish the whole work first?

Introduction / Context:
Partial-work information can be scaled to full-work times by proportion. The one with the smallest full-work time is the fastest. Convert each worker’s given partial completion into a per-day rate and then into the full time required for one job to objectively compare speeds.

Given Data / Assumptions:

• X does 1/4 work in 10 days ⇒ rate = (1/4)/10 = 1/40 job/day ⇒ full time = 40 days.
• Y does 40% = 2/5 in 40 days ⇒ rate = (2/5)/40 = 1/100 job/day ⇒ full time = 100 days.
• Z does 1/3 in 13 days ⇒ rate = (1/3)/13 = 1/39 job/day ⇒ full time ≈ 39 days.

Concept / Approach:
For each: full time = (given time) * (1 / given fraction). Compare 40, 100, and 39 days. The shortest time indicates the fastest worker in isolation.

Step-by-Step Solution:

Verification / Alternative check:
Rate comparison: 1/39 (Z) > 1/40 (X) > 1/100 (Y), so Z is indeed the fastest.

Why Other Options Are Wrong:
X is slightly slower than Z; Y is much slower. “Both X and Z” is incorrect because their times differ by 1 day.

Common Pitfalls:
Averaging days or fractions incorrectly. Always convert to either common rates or full times before comparing.

Final Answer:
Z