A and B invest ₹ 3,000 and ₹ 4,000, respectively. A also receives ₹ 10 per month as remuneration for running the business. The remaining profit is divided in the ratio of investments. If in one year A receives ₹ 390 in total, how much does B receive?

Introduction / Context:
This is a two-stage distribution: first, a fixed monthly amount to A for management; second, a proportional split of the remaining profit. We must separate these carefully to find B's portion.

Given Data / Assumptions:

• A's remuneration = ₹ 10 per month ⇒ ₹ 120 per year.
• A's total received = ₹ 390 (includes remuneration + share of remainder).
• Remainder is split in ratio 3,000 : 4,000 = 3 : 4.

Concept / Approach:
Deduct A's remuneration from A's total to get A's share from the remainder. Then back out the total remainder and compute B's share.

Step-by-Step Solution:
A's share from remainder = 390 − 120 = ₹ 270. Let remainder = T. A gets 3/7 of T = 270 ⇒ T = 270 * (7/3) = ₹ 630. Therefore, B gets 4/7 of T = (4/7)*630 = ₹ 360.

Verification / Alternative check:
A's total = remuneration 120 + share 270 = ₹ 390. Remainder 630 splits to 270 and 360; sums check.

Why Other Options Are Wrong:
₹ 630 is the whole remainder, not B's share. ₹ 480, ₹ 380, and ₹ 540 do not follow the 3 : 4 split from the computed remainder.

Common Pitfalls:
Treating ₹ 390 as A's share of the remainder only or splitting the entire profit before subtracting the fixed remuneration.

Final Answer:
₹ 360