A, B and C started a business with a total investment of '72000. A invests '6000 more than B and B invests 3000 less than C. If the total profit at the end of a years is '8640, find A's share.

Options

A. `'3240`
B. `'2520`
C. `'2880`
D. `'3360`

Answer

To solve the problem step by step, we will first define the investments of A, B, and C based on the information given.

### Step 1: Define the investments
Let the investment of B be \( x \). According to the problem:
- A invests \( 6000 \) more than B, so A's investment is \( x + 6000 \).
- B invests \( 3000 \) less than C, so C's investment is \( x + 3000 \).

### Step 2: Set up the equation for total investment
The total investment of A, B, and C is given as \( 72000 \). Therefore, we can write the equation:
\[ (x + 6000) + x + (x + 3000) = 72000 \]

### Step 3: Simplify the equation
Combining the terms, we have:
\[ 3x + 9000 = 72000 \]

### Step 4: Solve for \( x \)
Subtract \( 9000 \) from both sides:
\[ 3x = 72000 - 9000 \]
\[ 3x = 63000 \]
Now, divide by \( 3 \):
\[ x = 21000 \]

### Step 5: Calculate individual investments
Now that we have \( x \), we can find the investments of A, B, and C:
- B's investment: \( x = 21000 \)
- A's investment: \( x + 6000 = 21000 + 6000 = 27000 \)
- C's investment: \( x + 3000 = 21000 + 3000 = 24000 \)

### Step 6: Calculate the total profit share
The total profit is \( 8640 \). The profit is shared in the ratio of their investments:
- A's investment: \( 27000 \)
- B's investment: \( 21000 \)
- C's investment: \( 24000 \)

### Step 7: Find the total ratio
The total investment is:
\[ 27000 + 21000 + 24000 = 72000 \]
Now, let's find the ratio of their investments:
- A : B : C = \( 27000 : 21000 : 24000 \)

To simplify the ratio, we can divide each term by \( 3000 \):
\[ A : B : C = 9 : 7 : 8 \]

### Step 8: Calculate A's share of the profit
The total parts in the ratio are:
\[ 9 + 7 + 8 = 24 \]
A's share of the profit is:
\[ \text{A's share} = \frac{9}{24} \times 8640 \]

### Step 9: Solve for A's share
Calculating A's share:
\[ \text{A's share} = \frac{9 \times 8640}{24} \]
\[ = \frac{77760}{24} = 3240 \]

Thus, A's share of the profit is **Rs. 3240**.

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