Profit share of A is Rs .1200 out of total profit of Rs. 1800 and he had invested Rs .1600 more amount than B for 8 months while B invested his amount for a year. Find how much amount was invested by A (in Rs)?

Options

A. 2800
B. 1600
C. 2400
D. 1800

Answer

To find out how much amount was invested by A, we can follow these steps:

### Step 1: Determine the Profit Share of B
The total profit is Rs. 1800, and A's profit share is Rs. 1200. Therefore, B's profit share can be calculated as:
\[ \text{Profit share of B} = \text{Total Profit} - \text{Profit share of A} = 1800 - 1200 = 600 \]

### Step 2: Establish the Profit Sharing Ratio
Now, we can establish the profit sharing ratio between A and B:
\[ \text{Profit sharing ratio} = \text{A's share} : \text{B's share} = 1200 : 600 = 2 : 1 \]

### Step 3: Define the Investments
Let B's investment be Rs. x. According to the problem, A invested Rs. 1600 more than B. Therefore, A's investment can be expressed as:
\[ \text{A's investment} = x + 1600 \]

### Step 4: Account for the Time of Investment
A invested his amount for 8 months, while B invested for 12 months. The effective investment can be calculated by multiplying the amount invested by the time (in months):
\[ \text{Effective investment of A} = (x + 1600) \times 8 \]
\[ \text{Effective investment of B} = x \times 12 \]

### Step 5: Set Up the Equation Based on the Ratio
Since the profit sharing ratio is 2:1, we can set up the equation:
\[ \frac{(x + 1600) \times 8}{x \times 12} = \frac{2}{1} \]

### Step 6: Cross-Multiply to Solve for x
Cross-multiplying gives us:
\[ (x + 1600) \times 8 = 2 \times (x \times 12) \]
\[ 8x + 12800 = 24x \]

### Step 7: Rearrange the Equation
Rearranging the equation to isolate x:
\[ 12800 = 24x - 8x \]
\[ 12800 = 16x \]

### Step 8: Solve for x
Now, divide both sides by 16:
\[ x = \frac{12800}{16} = 800 \]

### Step 9: Calculate A's Investment
Now that we have the value of x, we can find A's investment:
\[ \text{A's investment} = x + 1600 = 800 + 1600 = 2400 \]

### Final Answer
Thus, the amount invested by A is Rs. 2400.

---