A & B invested in the Rs X and Rs`(X+800)` for same period time in a business .if A gets Rs 3200 as profit share out of total profit of Rs 6800, then find 'X' ?

Options

A. A)7800
B. B)6000
C. C)8400
D. D)6400

Answer

To solve the problem, we need to find the value of \( X \) given the profit shares of A and B. Let's break down the solution step by step.

### Step 1: Understand the investments
A invests \( X \) rupees, and B invests \( X + 800 \) rupees. Both invest for the same period of time.

### Step 2: Set up the profit-sharing ratio
The profit-sharing ratio is based on the amount invested. Therefore, the ratio of A's investment to B's investment is:
\[ \text{Ratio of A's investment to B's investment} = \frac{X}{X + 800} \]

### Step 3: Total profit and A's profit
The total profit is given as Rs 6800. A's share of the profit is Rs 3200.

### Step 4: Set up the equation
The ratio of A's profit to the total profit can be expressed as:
\[ \frac{A's \, profit}{Total \, profit} = \frac{3200}{6800} \]
This simplifies to:
\[ \frac{3200}{6800} = \frac{32}{68} = \frac{16}{34} = \frac{8}{17} \]

### Step 5: Equate the ratios
Since the profit-sharing ratio is the same as the investment ratio, we can set up the equation:
\[ \frac{X}{X + 800} = \frac{8}{17} \]

### Step 6: Cross-multiply to solve for \( X \)
Cross-multiplying gives us:
\[ 17X = 8(X + 800) \]
Expanding the right side:
\[ 17X = 8X + 6400 \]

### Step 7: Rearrange the equation
Now, we can rearrange the equation to isolate \( X \):
\[ 17X - 8X = 6400 \]
\[ 9X = 6400 \]

### Step 8: Solve for \( X \)
Dividing both sides by 9:
\[ X = \frac{6400}{9} \approx 711.11 \]

### Step 9: Check the options
Since the question asks for \( X \) in whole numbers, we can round it to the nearest whole number if necessary. However, based on the context of the problem, we can conclude that the value of \( X \) is approximately 711.

### Final Answer
Thus, the value of \( X \) is approximately Rs 711.

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