Wage sharing by efficiency: A completes a job in 12 days and B in 16 days. Working together they earn ₹ 2100. Divide the money fairly in proportion to work done by A and B.

Introduction / Context:
When multiple workers collaborate, a fair division of payment is proportional to each one’s contribution. For constant daily work rates, contribution is proportional to their rates, which are reciprocals of the individual completion times for the same job.

Given Data / Assumptions:

• A alone: 12 days ⇒ rate = 1/12 job/day.
• B alone: 16 days ⇒ rate = 1/16 job/day.
• Total payment = ₹ 2100; equal working duration.

Concept / Approach:
For a full job completed together, shares are in the ratio of rates 1/12 : 1/16 which simplifies to 16 : 12 = 4 : 3. Divide the total accordingly to get each worker’s fair compensation.

Step-by-Step Solution:

Verification / Alternative check:
The proportional-split method is equivalent to allocating wages by actual work done in any equal time interval, since work done is rate * time.

Why Other Options Are Wrong:
The other splits do not reflect the 4:3 ratio implied by 12 vs 16 days; “None” is unnecessary because a valid split exists.

Common Pitfalls:
Dividing equally or using time ratios directly instead of rate ratios (remember, rate is inverse of time).

Final Answer:
₹ 1200 to A, ₹ 900 to B