A, B, and C invest Rs. 2000, Rs. 3000, and Rs. 4000 in a business. After one year, A withdraws his money, but B and C continue for one more year. If the net profit after 2 years is Rs. 3200, what is A’s share?

Introduction / Context:
When investment durations differ, use capital × time to apportion profit. Here, A invests for 1 year, while B and C invest for 2 years.

Given Data / Assumptions:

• A = 2000 for 1 year.
• B = 3000 for 2 years.
• C = 4000 for 2 years.
• Total profit = Rs. 3200.

Concept / Approach:
Compute capital-year units, form the ratio, then allocate the profit accordingly.

Step-by-Step Solution:
A units = 2000 * 1 = 2000B units = 3000 * 2 = 6000C units = 4000 * 2 = 8000Total units = 2000 + 6000 + 8000 = 16000A’s share = 3200 * (2000/16000) = 3200 * (1/8) = Rs. 400

Verification / Alternative check:
Remaining profit for B and C = 3200 − 400 = Rs. 2800, split in the ratio 6000 : 8000 = 3 : 4 → Rs. 1200 and Rs. 1600; total checks out.

Why Other Options Are Wrong:
They reflect incorrect ratios or ignoring the extended investment durations of B and C.

Common Pitfalls:
Dividing profit simply in the ratio 2 : 3 : 4 (capitals) without accounting for time.

Final Answer:
Rs. 400