Three-worker job for ₹ 1110: A, B, and C finish alone in 12, 15, and 18 days respectively. If they share the proceeds fairly according to work done, what amount does C receive?

Introduction / Context:
Payment splitting among different rate workers is proportional to their rates, which are reciprocals of completion times. This problem asks specifically for the third worker’s share after all three work together on a fixed-price job.

Given Data / Assumptions:

• A: 12 days ⇒ rate = 1/12.
• B: 15 days ⇒ rate = 1/15.
• C: 18 days ⇒ rate = 1/18.
• Total payment = ₹ 1110; working together for equal time.

Concept / Approach:
Shares are proportional to the rates 1/12 : 1/15 : 1/18. Use a common denominator (e.g., 180) to convert to integer parts and then allocate the total amount based on those parts. The question asks for C’s amount only.

Step-by-Step Solution:

Verification / Alternative check:
A: 15/37 * 1110 = 450; B: 12/37 * 1110 = 360; C: 300; sum = 1110.

Why Other Options Are Wrong:
₹ 275, ₹ 335, and ₹ 339 do not match 10/37 of ₹ 1110; ₹ 320 is also off.

Common Pitfalls:
Using days directly instead of rates; always transform to rates before splitting.

Final Answer:
₹ 300