Three friends A, B, and C have taken loan from the bank and invested it in a partnership business. Further, they have made personal contribution of Rs 8,000, Rs 10,000 and Rs 12,000, respectively in the same business as well. At the end of the year they could pay the yearly return of Rs 5,000 to the bank out of their profit of Rs 13,400. Find the ratio of the remaining profit among these friends ?

Options

A. 2240, 2860, 3300
B. 2240, 2800, 3360
C. 2260, 2840, 3400
D. 2200, 2860, 3400

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Calculate the Remaining Profit
The total profit at the end of the year is given as Rs 13,400. Out of this, Rs 5,000 is paid to the bank as yearly return.

**Calculation:**
Remaining Profit = Total Profit - Yearly Return
Remaining Profit = 13,400 - 5,000 = 8,400

### Step 2: Determine the Personal Contributions
The personal contributions made by A, B, and C are as follows:
- A's contribution = Rs 8,000
- B's contribution = Rs 10,000
- C's contribution = Rs 12,000

### Step 3: Find the Ratio of Personal Contributions
To find the ratio of their contributions, we will express their contributions in simplest form:

**Calculation:**
The ratio of contributions is:
A : B : C = 8000 : 10000 : 12000

To simplify:
- Divide each term by 2000:
A : B : C = 4 : 5 : 6

### Step 4: Calculate the Shares of Remaining Profit
The remaining profit of Rs 8,400 will be divided among A, B, and C in the ratio of their contributions (4:5:6).

**Total parts in the ratio = 4 + 5 + 6 = 15 parts.**

Now, we can calculate each person's share:
- A's share = (4/15) * 8400
- B's share = (5/15) * 8400
- C's share = (6/15) * 8400

**Calculations:**
1. A's share:
A's share = (4/15) * 8400 = 2240

2. B's share:
B's share = (5/15) * 8400 = 2800

3. C's share:
C's share = (6/15) * 8400 = 3360

### Step 5: Write the Final Shares
- A's share = Rs 2,240
- B's share = Rs 2,800
- C's share = Rs 3,360

### Conclusion
The ratio of the remaining profit among A, B, and C is:
A : B : C = 2240 : 2800 : 3360

To simplify this ratio:
- Divide each part by 280:
A : B : C = 8 : 10 : 12
Dividing further by 2 gives:
A : B : C = 4 : 5 : 6

### Final Answer
The ratio of the remaining profit among A, B, and C is **4 : 5 : 6**.

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