A and B invest Rs. 12,000 and Rs. 16,000 respectively. After 8 months, C joins with Rs. 15,000. If the total profit after 2 years is Rs. 45,600, what is C’s share?

Introduction / Context:
Compute capital-months over the full 24 months. C joins 8 months after the start, so C’s contribution lasts for 16 months. Profit is apportioned in the ratio of capital × time for each partner.

Given Data / Assumptions:

• A: 12000 for 24 months.
• B: 16000 for 24 months.
• C: 15000 for 16 months (joined after 8 months).
• Total profit = Rs. 45600.

Concept / Approach:
Find capital-months and then C’s fraction of the total. Multiply by the profit to get the rupee share.

Step-by-Step Solution:
A units = 12000 * 24 = 288000B units = 16000 * 24 = 384000C units = 15000 * 16 = 240000Total units = 288000 + 384000 + 240000 = 912000C’s fraction = 240000/912000 = 5/19C’s share = 45600 * (5/19) = 2400 * 5 = Rs. 12000

Verification / Alternative check:
The simplification 45600/19 = 2400 makes the computation quick and exact.

Why Other Options Are Wrong:
Other amounts correspond to different fractions and do not match the 5/19 share.

Common Pitfalls:
Using 20 months for C incorrectly; ensure 24 − 8 = 16 months.

Final Answer:
Rs. 12000