A, B, and C enter into partnership. A invests some amount at the beginning, B invests double that amount after 6 months, and C invests thrice that amount after 8 months. If the annual profit is Rs. 18,000, what is C’s share?

Introduction / Context:
This is a classic capital–time allocation with staggered entries. Each partner’s effective contribution equals capital multiplied by the months it remained invested during the year.

Given Data / Assumptions:

• A invests x for 12 months.
• B invests 2x for the last 6 months.
• C invests 3x for the last 4 months (joined after 8 months).
• Total profit = Rs. 18000.

Concept / Approach:
Compute capital-months for each partner and compare. Surprisingly, all three turn out equal in this arrangement, resulting in equal profit shares.

Step-by-Step Solution:
A’s units = x * 12 = 12xB’s units = 2x * 6 = 12xC’s units = 3x * 4 = 12xHence A : B : C = 12x : 12x : 12x = 1 : 1 : 1C’s share = 18000 / 3 = Rs. 6000

Verification / Alternative check:
The symmetry confirms equal shares; any change in the joining months would upset the equality.

Why Other Options Are Wrong:
Other numbers do not reflect the equal capital-month contributions from all three partners.

Common Pitfalls:
Forgetting to multiply by months or incorrectly assuming direct proportionality to capital alone.

Final Answer:
Rs. 6000