Men and women wage comparison via work rates: 2 men + 1 woman finish a job in 14 days; 2 men + 4 women finish the same job in 8 days. If a man earns ₹ 60 per day, what should a woman be paid per day so that wages are proportional to productivity?

Introduction / Context:
When determining fair daily wages for different worker categories, the wage should reflect relative productivity. By comparing completion times for different team compositions, we can deduce each category’s daily work rate and then set pay accordingly.

Given Data / Assumptions:

• (2m + 1w)*14 = 1 job ⇒ 2m + w = 1/14.
• (2m + 4w)*8 = 1 job ⇒ 2m + 4w = 1/8.
• Man’s daily wage = ₹ 60; wages proportional to rate.

Concept / Approach:
Solve the linear system for m (man’s daily rate) and w (woman’s daily rate). Once w/m is known, multiply by ₹ 60 to get the woman’s fair daily wage.

Step-by-Step Solution:

Verification / Alternative check:
Check team rates: 2m + w = 2*(3/112) + 1/56 = 6/112 + 2/112 = 8/112 = 1/14; similarly 2m + 4w = 6/112 + 4/56 = 6/112 + 8/112 = 14/112 = 1/8.

Why Other Options Are Wrong:
₹ 30 and ₹ 35 undervalue productivity; ₹ 50 overpays relative to the solved rate; ₹ 45 is not supported by the linear system.

Common Pitfalls:
Dividing total days instead of solving the system, or equating wages to time rather than rate.

Final Answer:
₹ 40