Ankit ,Yogesh and Mahesh enter into a partnership business .Ankit invested 12000 Rs for the whole year , Yogesh invested 16000 Rs first and after of 4 month invested 4000 Rs more and Mahesh invested 15000 for first 9 months withdraw Rs 3000 after 9 months , if at the end of year Yogesh gets total profit of Rs 11200, then find the sum of total profit of Ankit and Mahesh . (in Rs)

Options

A. A)15110
B. B)15250
C. C)15570
D. D)15750

Answer

To solve the problem step by step, let's break down the investments and calculate the profits for Ankit, Yogesh, and Mahesh.

### Step 1: Calculate the effective capital contribution of each partner

1. **Ankit's Investment:**
- Amount: Rs 12,000
- Duration: 12 months
- Effective Capital = 12,000 * 12 = Rs 144,000

2. **Yogesh's Investment:**
- Initial Amount: Rs 16,000 for 4 months
- Additional Amount: Rs 4,000 for the remaining 8 months
- Effective Capital = (16,000 * 4) + (20,000 * 8)
- Effective Capital = 64,000 + 160,000 = Rs 224,000

3. **Mahesh's Investment:**
- Initial Amount: Rs 15,000 for 9 months
- Withdrawn Amount: Rs 3,000, leaving Rs 12,000 for the remaining 3 months
- Effective Capital = (15,000 * 9) + (12,000 * 3)
- Effective Capital = 135,000 + 36,000 = Rs 171,000

### Step 2: Calculate the profit-sharing ratio

Now we have the effective capital contributions:
- Ankit: Rs 144,000
- Yogesh: Rs 224,000
- Mahesh: Rs 171,000

The profit-sharing ratio is:
- Ankit : Yogesh : Mahesh = 144 : 224 : 171

### Step 3: Simplify the ratio

To simplify the ratio, we can divide each term by 1,000:
- Ankit: 144
- Yogesh: 224
- Mahesh: 171

### Step 4: Find the total parts of the ratio

Total parts = 144 + 224 + 171 = 539

### Step 5: Calculate Yogesh's share of profit

Given that Yogesh's profit is Rs 11,200, we can find the value of one part:
- Value of one part = Total profit / Total parts
- Value of one part = 11,200 / 224 = Rs 50

### Step 6: Calculate Ankit's and Mahesh's profits

1. **Ankit's Profit:**
- Ankit's share = 144 parts
- Ankit's Profit = 144 * 50 = Rs 7,200

2. **Mahesh's Profit:**
- Mahesh's share = 171 parts
- Mahesh's Profit = 171 * 50 = Rs 8,550

### Step 7: Calculate the sum of Ankit's and Mahesh's profits

Total profit of Ankit and Mahesh = Ankit's Profit + Mahesh's Profit
- Total profit = 7,200 + 8,550 = Rs 15,750

### Final Answer

The sum of the total profit of Ankit and Mahesh is Rs 15,750.

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