M,N and P invest X 50000 for a business M invests X 4000 more than N and N invests X 5000 more than P. Out of the total profit of X70000, what is the share received by MP.

Options

A. X29400
B. X30000
C. X 35000
D. X 40000

Answer

To solve the problem step by step, we will break down the investments of M, N, and P, and then calculate their shares from the total profit.

### Step 1: Define the investments
Let P's investment be \( K \).
- N invests \( K + 5000 \) (since N invests 5000 more than P).
- M invests \( K + 9000 \) (since M invests 4000 more than N).

### Step 2: Set up the equation for total investment
According to the problem, the total investment of M, N, and P is 50,000. Therefore, we can write the equation:
\[ K + (K + 5000) + (K + 9000) = 50000 \]

### Step 3: Simplify the equation
Combining the terms:
\[ K + K + 5000 + K + 9000 = 50000 \]
\[ 3K + 14000 = 50000 \]

### Step 4: Solve for K
Subtract 14000 from both sides:
\[ 3K = 50000 - 14000 \]
\[ 3K = 36000 \]
Now, divide by 3:
\[ K = \frac{36000}{3} = 12000 \]

### Step 5: Calculate individual investments
Now that we have \( K \), we can find the investments:
- P's investment: \( K = 12000 \)
- N's investment: \( K + 5000 = 12000 + 5000 = 17000 \)
- M's investment: \( K + 9000 = 12000 + 9000 = 21000 \)

### Step 6: Find the ratio of investments
The investments of M, N, and P are:
- M: 21000
- N: 17000
- P: 12000

The ratio of their investments is:
\[ M:N:P = 21000:17000:12000 \]
To simplify this, we can divide each term by 1000:
\[ M:N:P = 21:17:12 \]

### Step 7: Calculate the total profit share
The total profit is 70,000. To find M's share, we calculate:
\[ \text{M's share} = \frac{M's investment}{\text{Total investment}} \times \text{Total profit} \]
\[ \text{M's share} = \frac{21}{21 + 17 + 12} \times 70000 \]
\[ \text{M's share} = \frac{21}{50} \times 70000 \]
\[ \text{M's share} = 21 \times 1400 = 29400 \]

### Final Answer
M's share of the profit is **29,400**.

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