Partners A and B invest Rs 54,000 and Rs 90,000. Total profit is Rs 3,600, including A’s commission at a fixed percentage of total profit (as working partner). A receives Rs 1,800 in total. Find A’s commission as a percentage of total profit.

Introduction:
Working partners can receive a commission on total profit before the remaining profit is divided in the ratio of capital. We set up an equation in the commission rate using A’s total receipt and solve it algebraically.

Given Data / Assumptions:

• A invests 54,000; B invests 90,000
• Total profit = 3,600
• Let commission rate = r (on total profit)
• A’s total receipt = commission + share from remaining profit = 1,800

Concept / Approach:
Remaining profit after commission = 3,600 * (1 − r). A’s capital share fraction = 54,000 / (54,000 + 90,000) = 3/8 = 0.375. Form the equation: 3,600r + 0.375 * 3,600(1 − r) = 1,800.

Step-by-Step Solution:
Compute: 3,600r + 1,350(1 − r) = 1,800⇒ 3,600r + 1,350 − 1,350r = 1,800⇒ 2,250r = 450 ⇒ r = 0.2Commission percentage = 20%

Verification / Alternative check:
Commission = 720; remaining profit = 2,880; A’s share = 0.375 * 2,880 = 1,080; total to A = 720 + 1,080 = 1,800 (matches).

Why Other Options Are Wrong:
10%/5%/25% do not reproduce Rs 1,800 total.

Common Pitfalls:
Dividing the entire profit by capital ratios before deducting commission; miscomputing A’s fraction as 54/90 instead of 54/(54+90).

Final Answer:
20%