A, B and C enter into a partnership by investing a total of Rs 6000. A invests Rs 1000 and the remaining amount is invested by B and C in the ratio 2 : 3. If the annual profit is Rs 2400, what is the share of C in the profit?

Introduction / Context:
This is a straightforward partnership question in which three partners together invest a fixed total capital. One partner has a specified amount, and the remaining capital is divided between the other two in a given ratio. Since all partners remain in the business for the same period, profit sharing is directly proportional to their capital investment. The task is to determine the share of profit received by partner C from the total annual profit.

Given Data / Assumptions:
Total investment by A, B and C together is Rs 6000. A invests Rs 1000. The remaining investment of Rs 5000 is shared by B and C in the ratio 2 : 3. Total annual profit is Rs 2400. All partners are assumed to invest for the same duration of one year.

Concept / Approach:
When all partners remain in the business for the same time, their shares in the profit are proportional to their invested capital. First we compute the individual capital of B and C using the given ratio. Then we form the capital ratio of A, B and C. Finally we apply this ratio to the total profit to find the share that belongs to C. The key is to correctly handle the division of the remaining capital in the ratio 2 : 3.

Step-by-Step Solution:
Step 1: Total capital is Rs 6000, with A investing Rs 1000. Step 2: Remaining capital for B and C together is 6000 - 1000 = Rs 5000. Step 3: B and C share this 5000 in ratio 2 : 3. Step 4: Sum of ratio parts = 2 + 3 = 5 parts. Step 5: Value of 1 part = 5000 / 5 = Rs 1000. Step 6: Capital of B = 2 * 1000 = Rs 2000. Step 7: Capital of C = 3 * 1000 = Rs 3000. Step 8: Capital ratio A : B : C = 1000 : 2000 : 3000 = 1 : 2 : 3. Step 9: Total parts in ratio = 1 + 2 + 3 = 6 parts. Step 10: Each part of profit = 2400 / 6 = Rs 400. Step 11: Share of C = 3 parts = 3 * 400 = Rs 1200.

Verification / Alternative check:
We can verify by computing all shares. A gets 1 part, which is Rs 400. B gets 2 parts, which is Rs 800. C gets 3 parts, which is Rs 1200. The sum of these shares is 400 + 800 + 1200 = Rs 2400, exactly matching the total profit. The internal ratios 400 : 800 : 1200 simplify to 1 : 2 : 3, confirming that the computed share of C is consistent with the capitals and the total profit.

Why Other Options Are Wrong:
Rs 600 corresponds to only 1.5 parts in the ratio, which does not match the 3 parts assigned to C. Rs 1800 would give C an excessively large share relative to his capital. Rs 1950 does not fit any simple multiple of the base part value and would make the total profit different from Rs 2400. Only Rs 1200 correctly fits the capital ratio and adds up to the given profit.

Common Pitfalls:
Students sometimes mistakenly divide the total profit only in the ratio 2 : 3 between B and C, ignoring A. Another mistake is to divide Rs 6000 directly in the ratio 1 : 2 : 3 without first checking that A invests exactly Rs 1000. Carefully separating the known capital of A from the remaining capital and then applying the ratio 2 : 3 helps avoid these errors.

Final Answer:
The share of C in the annual profit is Rs 1200.