Equivalent efficiencies for man, woman, and boy: One man or two women or three boys can complete a job in 88 days. If one man, one woman, and one boy work together, in how many days will they finish the job?

Introduction / Context:
Statements like “one man or two women or three boys can finish in the same time” define fixed equivalence between individual rates. We convert to per-day rates for each category, then add the rates for one man, one woman, and one boy to get the combined rate and hence the time to complete the work together.

Given Data / Assumptions:

• 1 man finishes in 88 days ⇒ man’s rate rm = 1/88 job/day.
• 2 women finish in 88 days ⇒ each woman’s rate rw = 1/(88*2) = 1/176 job/day.
• 3 boys finish in 88 days ⇒ each boy’s rate rb = 1/(88*3) = 1/264 job/day.

Concept / Approach:
Combined rate = rm + rw + rb. Then time = 1 / (combined rate). Keep all fractions exact to avoid rounding errors, and simplify to an integer if possible.

Step-by-Step Solution:

Verification / Alternative check:
The equivalence implies 1 man ≡ 2 women ≡ 3 boys. So 1 man + 1 woman + 1 boy = 1 man + 0.5 man + 0.333… man = 1.833… man. Since 1 man takes 88 days, 1.833… man would take 88 / 1.833… = 48 days, consistent.

Why Other Options Are Wrong:
46, 54, 44, and 52 days do not reflect the exact combined rate 11/528.

Common Pitfalls:
Treating 1 man, 1 woman, 1 boy as equal contributors or miscomputing individual rates from the shared 88-day statement.

Final Answer:
48 days