Staggered departures on a contract: A, B and C can do a piece of work in 20, 24 and 30 days respectively. They contract the work for ₹ 5400 and start together, but B leaves 2 days before completion and C leaves 5 days before completion. What is A's share from the ₹ 5400?

Introduction / Context:
Here, not all workers stay for the full duration. We must first determine the total project duration from the staggered participation, then compute each person’s actual work amount. Finally, allocate the fixed ₹ 5400 proportional to these contributions. This mixes rate calculations with timeline reasoning.

Given Data / Assumptions:

• Rate(A) = 1/20; Rate(B) = 1/24; Rate(C) = 1/30
• B worked until 2 days before finish
• C worked until 5 days before finish
• Total remuneration = ₹ 5400

Concept / Approach:
Let total duration = T days. Then total work equals: T/20 + (T − 2)/24 + (T − 5)/30 = 1. Solve for T. Then compute A’s work fraction = T/20 and multiply by ₹ 5400 to get A’s share.

Step-by-Step Solution:
T/20 + (T − 2)/24 + (T − 5)/30 = 1Use denominator 120: (6T) + 5(T − 2) + 4(T − 5) all over 120 = 1⇒ (6T + 5T − 10 + 4T − 20) / 120 = 1 ⇒ (15T − 30) / 120 = 115T − 30 = 120 ⇒ 15T = 150 ⇒ T = 10 daysA’s work = T/20 = 10/20 = 1/2 of the jobA’s share = 1/2 * ₹ 5400 = ₹ 2700

Verification / Alternative check:
Compute B and C: B’s work = (T − 2)/24 = 8/24 = 1/3; C’s work = (T − 5)/30 = 5/30 = 1/6. Sum = 1/2 + 1/3 + 1/6 = 1 — perfect balance.

Why Other Options Are Wrong:
₹ 540, ₹ 600 are too small; ₹ 1800 understates A’s half-share.

Common Pitfalls:
Assuming all worked for T days; ignoring the early departures; arithmetic errors when clearing denominators.

Final Answer:
₹ 2700