If two men or three women or four boys can complete a job in 52 days, then how many days will one man, one woman, and one boy together take to complete the same job?

Introduction / Context:
This question uses equivalent worker groups to derive single-worker rates and then sums those rates for a mixed team. It is a standard application of work-rate addition.

Given Data / Assumptions:

• 2 men can finish in 52 days ⇒ group rate = 1/52 per day.
• 3 women can finish in 52 days.
• 4 boys can finish in 52 days.
• Find time for 1 man + 1 woman + 1 boy.

Concept / Approach:
Convert each to single-worker daily rate by dividing the group rate by the number in the group. Then add one man’s, one woman’s, and one boy’s daily rates, and invert to get the number of days.

Step-by-Step Solution:
Let total work = 1. 2 men rate = 1/52 ⇒ 1 man = 1/104 per day. 3 women rate = 1/52 ⇒ 1 woman = 1/156 per day. 4 boys rate = 1/52 ⇒ 1 boy = 1/208 per day. Mixed daily rate = 1/104 + 1/156 + 1/208 = 1/48. Hence days = 1 / (1/48) = 48 days.

Verification / Alternative check:
Common denominator arithmetic confirms 1/104 + 1/156 + 1/208 equals 1/48 exactly.

Why Other Options Are Wrong:
36, 40, 45 days or “none of these” do not match the exact rate sum inversion of 48 days.

Common Pitfalls:
Averaging the given days or people counts instead of converting to per-person rates; forgetting to invert the total rate for time.

Final Answer:
48 days