A and B are two partners and they have inversted ₹ 54,000 and ₹ 90,000 in a business. After one year A received ₹ 1800 as his share of profit out of total profit of ₹ 3600 including his certain commission on total profit, since he is a working partner and rest profit is received by B. What is the commission of A as a percentage of the total profit?

Options

A. `20%`
B. `10%`
C. `5%`
D. `25%`

Answer

To solve the problem step by step, we need to determine A's commission as a percentage of the total profit. Let's break it down:

### Step 1: Determine the total investment of A and B
A's investment = ₹ 54,000
B's investment = ₹ 90,000

### Step 2: Calculate the total profit
Total profit = ₹ 3,600

### Step 3: Determine the profit-sharing ratio
To find the profit-sharing ratio, we multiply each partner's investment by the time they invested (which is 12 months for both in this case).

- A's share of investment = ₹ 54,000 * 12 = ₹ 648,000
- B's share of investment = ₹ 90,000 * 12 = ₹ 1,080,000

Now, we can find the ratio of their investments:
- Ratio of A to B = 648,000 : 1,080,000
- Simplifying this ratio:
- Divide both sides by 216,000 (the GCD):
- A : B = 3 : 5

### Step 4: Calculate A's share of the profit based on the ratio
Total parts = 3 + 5 = 8 parts
A's share of profit = (3/8) * Total profit
A's share of profit = (3/8) * ₹ 3,600 = ₹ 1,350

### Step 5: Determine A's commission
A received ₹ 1,800 as his share of profit, which includes his commission.
We already calculated A's share of profit without commission as ₹ 1,350.
Thus, A's commission = Total amount received by A - A's share of profit
A's commission = ₹ 1,800 - ₹ 1,350 = ₹ 450

### Step 6: Calculate A's commission as a percentage of the total profit
To find the percentage of A's commission with respect to the total profit:
Percentage of A's commission = (A's commission / Total profit) * 100
Percentage of A's commission = (₹ 450 / ₹ 3,600) * 100
Percentage of A's commission = 12.5%

### Final Answer
A's commission as a percentage of the total profit is **12.5%**.

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