A and B entered into a business my making investment of Rs 2400 and 2800 respectively .After six months A left the business and after four more months C joined the business with capital 20 % more than A's investment .If at the end of year sum of profit share of A and C is Rs 4200 ,then find total profit ?

Options

A. A)10200 Rs
B. B)11200 Rs
C. C)11800 Rs
D. D)10800 Rs

Answer

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

### Step 1: Determine the investments of A, B, and C
- A's investment = Rs 2400
- B's investment = Rs 2800
- C's investment = 20% more than A's investment.

Calculating C's investment:
\[ C's\ investment = A's\ investment + 20\% \ of\ A's\ investment \]
\[ C's\ investment = 2400 + 0.2 \times 2400 = 2400 + 480 = Rs\ 2880 \]

### Step 2: Calculate the time of investment for each partner
- A invests for 6 months.
- B invests for 12 months (1 year).
- C joins after A leaves, so C invests for 2 months (from month 7 to month 12).

### Step 3: Calculate the effective capital contribution (Investment × Time)
- A's contribution = \( 2400 \times 6 = 14400 \)
- B's contribution = \( 2800 \times 12 = 33600 \)
- C's contribution = \( 2880 \times 2 = 5760 \)

### Step 4: Find the total contribution
Now we will find the total contributions:
- Total contribution = A's contribution + B's contribution + C's contribution
\[ Total\ contribution = 14400 + 33600 + 5760 = 53760 \]

### Step 5: Find the profit-sharing ratio
Now we will find the profit-sharing ratio based on their contributions:
- A's share = 14400
- B's share = 33600
- C's share = 5760

To find the ratio:
- A : B : C = 14400 : 33600 : 5760
- Simplifying this ratio:
- Divide each term by 1440:
\[ A : B : C = 10 : 23.33 : 4 \]
- To make it whole numbers, we can multiply by 3:
\[ A : B : C = 30 : 70 : 12 \]

### Step 6: Calculate the total profit
We know from the problem that the sum of A and C's profit share is Rs 4200.
- A's share + C's share = 30x + 12x = 42x
- Given that 42x = 4200, we can find x:
\[ x = \frac{4200}{42} = 100 \]

### Step 7: Find the total profit
Now we can find the total profit:
- Total profit = A's share + B's share + C's share
- A's share = 30x = 3000
- B's share = 70x = 7000
- C's share = 12x = 1200
- Total profit = 3000 + 7000 + 1200 = 11200

### Final Answer
The total profit is Rs 11200.

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