Man–boy combined wages: A man and a boy together earn ₹ 800 for 5 days. The man’s efficiency is three times the boy’s. What is the boy’s daily wage if pay is proportional to work done?

Introduction / Context: When two workers have known relative efficiencies and work for the same time, their wage split should match their relative work contributions. From the total payment over 5 days, we can deduce the boy’s 5-day share and then his daily wage.

Given Data / Assumptions:

• Total pay for 5 days together = ₹ 800.
• Man’s efficiency = 3 × boy’s efficiency.
• Payment proportional to work contributed.

Concept / Approach: Let the boy’s one-day work be 1 unit; then the man’s is 3 units. Together they produce 4 units per day. Over 5 days they produce 20 units. Split ₹ 800 in the ratio 3:1 per day, which is the same as 15:5 over 5 days. The boy receives one-fourth of the total because he contributes 1 out of 4 units each day.

Step-by-Step Solution:

Verification / Alternative check: Man’s 5-day share = 600 ⇒ daily = 120; 120 is exactly three times 40, consistent with the efficiency ratio.

Why Other Options Are Wrong: ₹ 56 and ₹ 44 overvalue; ₹ 76 is unrelated; ₹ 60 conflicts with the 3:1 efficiency ratio when combined with boy’s daily rate.

Common Pitfalls: Splitting ₹ 800 equally or forgetting to divide the boy’s 5-day share by 5 to get the daily wage.

Final Answer: ₹ 40