Sunil invested Rs `(x+2000)` and Anil invested Rs . `(x+3000)` in a partnership . If profit at the end of the year is Rs . 48000 and value of Anil's share in it is Rs. 28000, then find the value of x ? (in Rs )

Options

A. 500
B. 400
C. 600
D. 800

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step 1: Define the Investments
Let Sunil's investment be \( S = x + 2000 \) and Anil's investment be \( A = x + 3000 \).

### Step 2: Total Profit and Anil's Share
The total profit at the end of the year is Rs. 48000. Anil's share of the profit is Rs. 28000. Therefore, Sunil's share of the profit is:
\[ \text{Sunil's Share} = \text{Total Profit} - \text{Anil's Share} = 48000 - 28000 = 20000 \]

### Step 3: Set Up the Ratio of Investments to Profits
Since the time period for both investments is the same, the ratio of their investments is equal to the ratio of their profits. Thus, we can set up the following equation:
\[ \frac{S}{A} = \frac{\text{Sunil's Share}}{\text{Anil's Share}} = \frac{20000}{28000} \]

### Step 4: Simplify the Profit Ratio
We can simplify the ratio of profits:
\[ \frac{20000}{28000} = \frac{5}{7} \]

### Step 5: Substitute the Investments into the Ratio
Now substituting the investments into the ratio:
\[ \frac{x + 2000}{x + 3000} = \frac{5}{7} \]

### Step 6: Cross Multiply to Solve for x
Cross multiplying gives us:
\[ 7(x + 2000) = 5(x + 3000) \]

### Step 7: Expand Both Sides
Expanding both sides:
\[ 7x + 14000 = 5x + 15000 \]

### Step 8: Rearrange the Equation
Rearranging the equation to isolate \( x \):
\[ 7x - 5x = 15000 - 14000 \]
\[ 2x = 1000 \]

### Step 9: Solve for x
Dividing both sides by 2 gives:
\[ x = 500 \]

### Final Answer
The value of \( x \) is Rs. 500.

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