Daily wages with different days worked: A, B, and C complete a work costing ₹ 1800. They work for 6, 4, and 9 days respectively, and their daily wage rates are in the ratio 5 : 6 : 4. How much should A receive?

Introduction / Context:
When workers have different daily wage rates and work for different numbers of days, their total payments are proportional to (daily rate) * (days worked). With the cost of the work fixed, divide the total amount in this compound proportion to determine each person’s due amount.

Given Data / Assumptions:

• Daily wage ratio A : B : C = 5 : 6 : 4.
• Days worked A = 6, B = 4, C = 9.
• Total payment = ₹ 1800.

Concept / Approach:
Compute proportional “earnings units” as (rate factor) * (days). Sum across all three to get total units, then allocate the ₹ 1800 according to each worker’s units. A’s amount is what is requested.

Step-by-Step Solution:

Verification / Alternative check:
B’s amount = 24 * 20 = ₹ 480; C’s = 36 * 20 = ₹ 720; total = ₹ 1800.

Why Other Options Are Wrong:
₹ 500, ₹ 450, and ₹ 700 do not equal 30 units at ₹ 20 per unit; ₹ 900 is too high given the unit breakdown.

Common Pitfalls:
Dividing simply by days or by the rate ratio alone; the correct approach multiplies both factors.

Final Answer:
₹ 600