The efficiencies (work rates) of A, B, and C are in the ratio 6 : 5 : 4. If they receive a total of ₹ 27000 for completing the job and payment is distributed in proportion to individual work done, what is C’s share?

Introduction / Context: When people work together for the same duration, the share of wages proportional to work done equals the ratio of their efficiencies. This question directly applies proportional division.

Given Data / Assumptions:

• Efficiency ratio A : B : C = 6 : 5 : 4.
• Total payment = ₹ 27000.
• They all work for the same time period.

Concept / Approach: If time is common, work done by each ∝ efficiency. Hence, payment shares are in the same ratio 6 : 5 : 4. Sum the parts and allocate to C accordingly.

Step-by-Step Solution: Total parts = 6 + 5 + 4 = 15. C’s share = (4/15) * 27000 = 4 * 1800 = ₹ 7200.

Verification / Alternative check: A’s share = (6/15)*27000 = ₹ 10800; B’s share = (5/15)*27000 = ₹ 9000; C’s share = ₹ 7200. Sum = 10800 + 9000 + 7200 = ₹ 27000. Correct.

Why Other Options Are Wrong: ₹ 2700, ₹ 6300, ₹ 6000, ₹ 14400 do not match the proportional split with ratio 6 : 5 : 4 on ₹ 27000.

Common Pitfalls: Dividing equally instead of proportionally, or mixing up the ratio order for A, B, and C.

Final Answer: ₹ 7200