Work and wages — man vs. boy sharing based on efficiency (5 days): A man and a boy together earn total wages of $800 for 5 days of joint work. The man's efficiency is three times the boy's efficiency. Assuming wages are shared in direct proportion to work done per day, what are the boy's daily wages (in dollars per day)?

Introduction / Context:
This problem from work-and-wages tests proportional sharing. When workers have different efficiencies, their wage shares are divided in the same ratio as their effective work contributions. The question asks for the boy's daily wage given the total pay for 5 days and a stated efficiency ratio.

Given Data / Assumptions:

• Total wages for 5 days together = $800.
• Man's efficiency : Boy's efficiency = 3 : 1.
• Payment is proportional to work done (standard assumption in wage-sharing problems).
• We need the boy's daily wage in dollars per day.

Concept / Approach:
If the boy's work rate is b units/day, the man's is 3b units/day. Together per day they contribute 4b units. Over 5 days, total work = 5 * 4b = 20b units. Wages split in the ratio of their contributions: man gets 3/4 of the total and boy gets 1/4 of the total. Then divide the boy's 5-day share by 5 to obtain his daily wage.

Step-by-Step Solution:
Work rates: boy = b, man = 3b.Daily combined rate = b + 3b = 4b.Total wages for 5 days = $800.Share ratio = 3 : 1 ⇒ Boy's share = (1/4) * 800 = $200 for 5 days.Boy's daily wage = 200 / 5 = $40 per day.

Verification / Alternative check:
If the boy earns $40/day, in 5 days he gets $200 and the man gets $600. That respects the 3:1 split and sums to $800, consistent with the prompt.

Why Other Options Are Wrong:

• $44 and $56 break the exact 3:1 sharing for a total of $800 in 5 days.
• $76 is far too high for the boy given he does only one quarter of the work.

Common Pitfalls:

• Dividing by 5 too early (before applying the share) or mixing up man/boy ratios.

Final Answer:
$40