A, B and C started a business with investments of ₹1600,₹2100 , ₹1500 respectively. After 8 months from the start of the business, B and C invested additional amounts in the ratio of 3:5 respectively. If the ratio of total annual profit to C's share in the annual profit was 3:1 then what was the additional amount invested by B after 8 months?

Options

A. ₹1200
B. ₹600
C. ₹900
D. ₹300

Answer

To solve the problem, we need to follow these steps:

### Step 1: Calculate the initial investments and their time contributions
A, B, and C invested ₹1600, ₹2100, and ₹1500 respectively. They invested for different durations:
- A's investment duration: 12 months (since he invested from the start)
- B's investment duration: 12 months
- C's investment duration: 12 months

The contributions to the profit can be calculated as:
- A's contribution = ₹1600 * 12 = ₹19200
- B's contribution = ₹2100 * 12 = ₹25200
- C's contribution = ₹1500 * 12 = ₹18000

### Step 2: Calculate the total contributions after 8 months
After 8 months, B and C invest additional amounts in the ratio of 3:5. Let’s denote the additional amounts invested by B and C as 3x and 5x respectively.

Now, we calculate the contributions for B and C after 8 months:
- B's contribution for the first 8 months = ₹2100 * 8 = ₹16800
- C's contribution for the first 8 months = ₹1500 * 8 = ₹12000

After 8 months, their total contributions will be:
- B's total contribution = ₹16800 + (3x * 4) (since B's additional investment will be for 4 months)
- C's total contribution = ₹12000 + (5x * 4) (since C's additional investment will be for 4 months)

### Step 3: Set up the equation for the total profit
The total profit contributions can be calculated as:
- A's total contribution = ₹19200
- B's total contribution = ₹16800 + 12x (since 3x for 4 months)
- C's total contribution = ₹12000 + 20x (since 5x for 4 months)

Thus, the total contributions will be:
Total = ₹19200 + (₹16800 + 12x) + (₹12000 + 20x)

### Step 4: Use the ratio of total profit to C's share
According to the problem, the ratio of total annual profit to C's share in the annual profit is 3:1. Therefore, we can say:
Total Profit = 3 * C's share

C's share can be calculated from C's total contribution:
C's share = ₹12000 + 20x

### Step 5: Set up the equation
Now we can set up the equation:
Total Profit = ₹19200 + ₹16800 + ₹12000 + 32x = ₹48000 + 32x

According to the ratio:
3 * (₹12000 + 20x) = ₹48000 + 32x

### Step 6: Solve for x
Expanding the equation:
₹36000 + 60x = ₹48000 + 32x
=> 60x - 32x = ₹48000 - ₹36000
=> 28x = ₹12000
=> x = ₹12000 / 28
=> x = ₹428.57 (approximately)

### Step 7: Calculate the additional amount invested by B
The additional amount invested by B is:
3x = 3 * ₹428.57 = ₹1285.71 (approximately)

### Final Answer
Therefore, the additional amount invested by B after 8 months is approximately ₹1285.71.

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