Three-worker contract sharing: A, B, and C agree to do a job for ₹ 4200. Their individual times are 6 days, 10 days, and 12 days respectively. If all three work together, what are the fair shares of A, B, and C from ₹ 4200?

Introduction / Context:
For workers collaborating on a fixed-price job, payment is split proportional to work done, which in turn is proportional to each worker’s constant daily rate. Rates are reciprocals of their individual completion times for the same job.

Given Data / Assumptions:

• A alone: 6 days ⇒ rate = 1/6.
• B alone: 10 days ⇒ rate = 1/10.
• C alone: 12 days ⇒ rate = 1/12.
• Total payment = ₹ 4200; equal working duration together.

Concept / Approach:
Compute the rate ratio, convert to integer parts, and then divide the total payment accordingly. Using a common denominator helps to avoid fractional parts.

Step-by-Step Solution:

Verification / Alternative check:
The shares add to ₹ 4200 and respect the relative productivities.

Why Other Options Are Wrong:
Only the option with (₹ 2000, ₹ 1200, ₹ 1000) matches the exact 10:6:5 ratio derived from the given times.

Common Pitfalls:
Using days as the ratio rather than rates; remember the faster worker gets more due to higher rate.

Final Answer:
₹ 2000, ₹ 1200, ₹ 1000