Ram, Shyam, and Kamal invest in the ratio 3 : 4 : 7. If the annual profit is Rs. 21,000, what is Kamal’s share?

Introduction / Context:
Profit shares in partnership with equal time are directly proportional to capitals. With the ratio given, we compute Kamal’s fraction of the total and multiply by the total profit to obtain his share.

Given Data / Assumptions:

• Capital ratio = 3 : 4 : 7 (Ram : Shyam : Kamal).
• Total profit = Rs. 21,000.
• Time period is the same for all.

Concept / Approach:
Kamal’s fraction = 7 / (3 + 4 + 7) = 7 / 14 = 1/2. Kamal’s share = 1/2 of the total profit.

Step-by-Step Solution:
Sum of ratio parts = 3 + 4 + 7 = 14. Kamal’s fraction = 7 / 14 = 1/2. Kamal’s share = (1/2) * 21,000 = Rs. 10,500.

Verification / Alternative check:
Remaining Rs. 10,500 splits between Ram and Shyam in 3 : 4 (4,500 and 6,000), and totals reconcile to Rs. 21,000.

Why Other Options Are Wrong:
Rs. 12,500 and Rs. 15,000 exceed Kamal’s exact half; Rs. 10,000 is too low.

Common Pitfalls:
Not summing all ratio parts before computing the fraction, or mixing up which partner corresponds to 7 parts.

Final Answer:
₹ 10500