Aakash and Vikash invested Rs `(x+2000)` and Rs `(x+3000)` respectively in a partenership . If profit at the end of the year is Rs 28000 and value of Vikash's share is Rs 16000, what is the value of x ? (in Rs)

Options

A. A)1500
B. B)1000
C. C)2000
D. D)500

Answer

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

### Step 1: Identify the investments
Aakash's investment = \( x + 2000 \)
Vikash's investment = \( x + 3000 \)

### Step 2: Set up the profit ratio
The total profit at the end of the year is Rs 28000, and Vikash's share of the profit is Rs 16000. Therefore, Aakash's share of the profit can be calculated as:
\[ \text{Aakash's share} = 28000 - 16000 = 12000 \]

### Step 3: Determine the ratio of their profits
The ratio of Aakash's profit to Vikash's profit is:
\[ \text{Aakash's profit} : \text{Vikash's profit} = 12000 : 16000 = 3 : 4 \]

### Step 4: Set up the equation based on the investment ratio
The ratio of their investments should also be equal to the ratio of their profits:
\[ \frac{x + 2000}{x + 3000} = \frac{3}{4} \]

### Step 5: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 4(x + 2000) = 3(x + 3000) \]

### Step 6: Expand both sides
Expanding both sides results in:
\[ 4x + 8000 = 3x + 9000 \]

### Step 7: Rearrange the equation to solve for x
Now, we can rearrange the equation:
\[ 4x - 3x = 9000 - 8000 \]
\[ x = 1000 \]

### Conclusion
The value of \( x \) is Rs 1000.

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