In the year 2019, R has invested for six months only while Q and P invested for the whole year. Find the total profit earned during the year 2019.

Steps to Solve

1. Read Data from the Table

   From the table, we can see the profit earned by each partner in various years. For 2019:

   • Profit by P: $6400$
   • Profit by R: Not specified (let's denote it as $R$)
   • Profit by Q: Not specified (let's denote it as $Q$)

2. Understand Total Profit for 2019

   The total profit for 2019 is given as $19200$. We can express this as an equation: $$ 6400 + R + Q = 19200 $$

3. Calculate the Total Profit Contribution by R and Q

   Rearranging the equation gives us: $$ R + Q = 19200 - 6400 $$ $$ R + Q = 12800 $$

4. Determine the Investments for 2019

   The problem states that R invested for 6 months, while Q and P invested for the whole year. Assuming equal share in profit based on the investment, we need to break down the contributions.

5. Equitable Distribution of Profit

   Given that:

   • P invested for 12 months
   • Q invested for 12 months
   • R invested for 6 months

   We can calculate the ratio of their investments as follows:

   • Total months of investment = $P: 12 + Q: 12 + R: 6 = 30$
   • P's share: $12/30$, Q’s share: $12/30$, R’s share: $6/30$

6. Express Individual Shares in Terms of Total Profit

   Assigning the total profit among the partners based on the share:

   • P's profit share: $$ P's , Share = 19200 \times \frac{12}{30} = 7680 $$

   • Q's profit share: $$ Q's , Share = 19200 \times \frac{12}{30} = 7680 $$

   • R's profit share: $$ R's , Share = 19200 \times \frac{6}{30} = 3840 $$