Three workers together: Amit, Vipul, and Kapil complete a job in 12, 16, and 24 days respectively. If they earn ₹ 2700 for the job, what is Vipul’s share under a fair division?

Introduction / Context: For three workers with different individual completion times, their rates determine their shares in a combined job. The fair split is proportional to rates, i.e., inverses of their days to finish alone.

Given Data / Assumptions:

• Amit: 12 days ⇒ rate = 1/12.
• Vipul: 16 days ⇒ rate = 1/16.
• Kapil: 24 days ⇒ rate = 1/24.
• Total payment = ₹ 2700.

Concept / Approach: Convert rates to integer parts using a common denominator (e.g., 48): 4, 3, and 2 parts respectively. Vipul’s share corresponds to 3 out of the total (4 + 3 + 2) = 9 parts of the payment.

Step-by-Step Solution:

Verification / Alternative check: Amit’s share = 4/9 * 2700 = 1200; Kapil’s share = 2/9 * 2700 = 600; sums to ₹ 2700.

Why Other Options Are Wrong: ₹ 450 and ₹ 225 are too small (half or quarter of the correct value). ₹ 1000 and ₹ 800 do not match the exact 3/9 fraction.

Common Pitfalls: Using days instead of rates; always invert days to get parts for fair division.

Final Answer: ₹ 900