X,Y and Z invested `₹ 14000` in total in a business. X invested `₹3120` more than Y and Z invested `₹1720` less than Y. The total profit was `₹ 35000`. Find the share of Z.

Options

A. `₹ 8100`
B. `₹ 6200`
C. `₹ 7280`
D. `₹ 7040`

Explanation

To solve the problem step by step, we will break down the investments of X, Y, and Z based on the information provided and then calculate Z's share of the profit.

### Step 1: Define the Variables
Let:
- Y's investment = ₹Y
- X's investment = Y + ₹3120 (since X invested ₹3120 more than Y)
- Z's investment = Y - ₹1720 (since Z invested ₹1720 less than Y)

### Step 2: Set Up the Equation
According to the problem, the total investment of X, Y, and Z is ₹14000. Therefore, we can write the equation:
\[ X + Y + Z = 14000 \]
Substituting the values of X and Z in terms of Y, we get:
\[ (Y + 3120) + Y + (Y - 1720) = 14000 \]

### Step 3: Simplify the Equation
Combine like terms:
\[ Y + 3120 + Y + Y - 1720 = 14000 \]
This simplifies to:
\[ 3Y + 1400 = 14000 \]

### Step 4: Solve for Y
Now, isolate Y:
\[ 3Y = 14000 - 1400 \]
\[ 3Y = 12600 \]
\[ Y = \frac{12600}{3} = 4200 \]

### Step 5: Calculate X and Z's Investments
Now that we have Y's investment, we can find X and Z's investments:
- X's investment:
\[ X = Y + 3120 = 4200 + 3120 = 7320 \]
- Z's investment:
\[ Z = Y - 1720 = 4200 - 1720 = 2480 \]

### Step 6: Calculate the Profit Share
The total profit is ₹35000. The profit share is distributed in the same ratio as their investments. The total investment is:
\[ X + Y + Z = 7320 + 4200 + 2480 = 14000 \]

The ratio of their investments is:
- X : Y : Z = 7320 : 4200 : 2480

To find Z's share of the profit, we first calculate the total parts of the ratio:
\[ Total\ Parts = 7320 + 4200 + 2480 = 14000 \]

Now, Z's share of the profit can be calculated as:
\[ Z's\ Share = \left(\frac{Z's\ Investment}{Total\ Investment}\right) \times Total\ Profit \]
\[ Z's\ Share = \left(\frac{2480}{14000}\right) \times 35000 \]
\[ Z's\ Share = \frac{2480 \times 35000}{14000} = 6200 \]

### Final Answer
Thus, Z's share of the profit is **₹6200**.

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