X y z start a web based venture together X invest 50000 rupees for 5 month . Y invest 70000 for 5 month and Z invest 40000 for 10 month. in the first year the venture makes a profit of 2 lakh. a part of profit is shared between Y and Z in ratio of 2 ratio 3 and profit is dividing divided among X, Y and Z in ratio of their initial investments. the amount that Z receives is 4 times the amount that X receives. how much amount does Y recieves?

Let's break down the problem and solve it step by step.

### Step 1: Calculate the total effective investments
Each person invests money for different periods, so we need to calculate the effective investments by multiplying the amount of money they invest by the number of months they invest for.

- **X's effective investment**:  
  \( 50,000 \times 5 = 250,000 \) rupees

- **Y's effective investment**:  
  \( 70,000 \times 5 = 350,000 \) rupees

- **Z's effective investment**:  
  \( 40,000 \times 10 = 400,000 \) rupees

Now, the total effective investment is:
\[
250,000 + 350,000 + 400,000 = 1,000,000 \text{ rupees}
\]

### Step 2: Set up profit sharing ratio
The profit is to be divided in the ratio of their effective investments. Thus, the ratio in which the profit is divided among X, Y, and Z is:
\[
\text{X : Y : Z} = 250,000 : 350,000 : 400,000 = 25 : 35 : 40
\]

Let the total profit be denoted by \( P = 2,00,000 \) rupees.

The part of the profit that is divided among X, Y, and Z is given in the ratio of their investments. Also, it is mentioned that Z receives 4 times the amount that X receives.

### Step 3: Set up an equation for the amounts received by X, Y, and Z
Let the amount received by X be \( x \).  
Then, according to the problem, the amount received by Z is \( 4x \).

The ratio of X to Z is \( 25:40 \), which simplifies to \( 5:8 \). Therefore:
\[
\frac{Z}{X} = \frac{8}{5}
\]
Thus, if \( X \) receives \( x \), then \( Z \) must receive \( 8x \).



X, Y, and Z start a web-based venture together. X invests 50,000 rupees for 5 months, Y invests 70,000 for 5 months, and Z invests 40,000 for 10 months. In the first year, the venture makes a profit of 2 lakh rupees. A part of the profit is shared between Y and Z in the ratio of 2:3, and the profit is divided among X, Y, and Z in the ratio of their initial investments. Z receives 4 times the amount X receives. How much does Y receive?

Solve a profit distribution problem where three partners invest varying amounts for different durations. Learn how to calculate the effective investment, set up the ratio of profit distribution, and determine the amount each partner receives. This example is ideal for students in Grades 8-10, focusing on ratios, proportions, and investment-related concepts.

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