Man–boy wages with 6:1 efficiency: A man and a boy earn ₹ 1400 for 10 days of joint work. If the man’s efficiency is six times the boy’s and wages are proportional to work done, what is the boy’s daily wage?

Introduction / Context:
Relative efficiency determines how total pay should be split among workers who work together for equal time. Once the boy’s total share over 10 days is found from the ratio, the daily wage is the share divided by 10.

Given Data / Assumptions:

• Total pay for 10 days together = ₹ 1400.
• Efficiency ratio (man : boy) = 6 : 1.
• Wages proportional to work done.

Concept / Approach:
With efficiency 6:1, the wage ratio is also 6:1. Thus the boy’s fraction is 1/7 of the total. Compute the boy’s 10-day share and divide by 10 to get his daily wage.

Step-by-Step Solution:

Verification / Alternative check:
Man’s daily wage would then be 6 times ₹ 20 = ₹ 120. Over 10 days: ₹ 1200; plus boy’s ₹ 200 equals ₹ 1400 total.

Why Other Options Are Wrong:
₹ 10 and ₹ 15 are too low; ₹ 30 and ₹ 25 are too high given the exact 6:1 ratio and total amount.

Common Pitfalls:
Splitting equally or forgetting to divide the boy’s multi-day share by the number of days.

Final Answer:
₹ 20