A,B,C start business with investment `₹4200,₹3600 ,₹2400` after 4 months from start , A invested `₹1000`, after 6 months B,C invest in ratio 1:2 if at end of 10 months profit is `₹2820` and A's profit was `₹1200` what was additional amount B invested

Options

A. `₹800`
B. `₹200`
C. `₹500`
D. `₹400`

Answer

To solve the problem step-by-step, we need to analyze the investments made by A, B, and C, and how the profits are distributed based on their investments over time.

### Step 1: Calculate the initial investments and time periods
- A's initial investment = ₹4200
- B's initial investment = ₹3600
- C's initial investment = ₹2400

### Step 2: Calculate the effective investment of A
- A invests ₹4200 for the first 4 months.
- After 4 months, A invests an additional ₹1000, making it ₹5200 for the remaining 6 months.
- Total investment by A = (₹4200 * 4 months) + (₹5200 * 6 months) = ₹16800 + ₹31200 = ₹48000.

### Step 3: Calculate the effective investment of B
- B invests ₹3600 for the first 6 months.
- After 6 months, B invests an additional amount (let's call it ₹X) for the remaining 4 months.
- Total investment by B = (₹3600 * 6 months) + (₹X * 4 months) = ₹21600 + ₹4X.

### Step 4: Calculate the effective investment of C
- C invests ₹2400 for the first 6 months.
- After 6 months, C invests in the ratio of 1:2 with B, meaning if B invests ₹X, C invests ₹2X.
- Total investment by C = (₹2400 * 6 months) + (₹2X * 4 months) = ₹14400 + ₹8X.

### Step 5: Calculate total investment and profit distribution
- Total investment = A's investment + B's investment + C's investment
- Total investment = ₹48000 + (₹21600 + ₹4X) + (₹14400 + ₹8X)
- Total investment = ₹48000 + ₹21600 + ₹14400 + ₹12X = ₹84000 + ₹12X.

### Step 6: Determine the profit share
- Total profit = ₹2820.
- A's profit = ₹1200.
- The profit share is proportional to their investments.

### Step 7: Set up the equation for A's profit
- A's profit share = (A's investment / Total investment) * Total profit
- ₹1200 = (₹48000 / (₹84000 + ₹12X)) * ₹2820.

### Step 8: Solve for X
1. Rearranging the equation:
\[ 1200 * (₹84000 + ₹12X) = ₹48000 * ₹2820 \]
2. Simplifying:
\[ 1200 * ₹84000 + 1200 * 12X = ₹135360000 \]
3. Calculate ₹1200 * ₹84000:
\[ 100800000 + 14400X = 135360000 \]
4. Rearranging gives:
\[ 14400X = 135360000 - 100800000 \]
\[ 14400X = 34480000 \]
5. Solving for X:
\[ X = \frac{34480000}{14400} = 2400. \]

### Step 9: Calculate the additional amount B invested
- The additional amount B invested = ₹X = ₹2400.

### Final Answer
The additional amount B invested is ₹2400.