P and Q entered a partnership for 3 yr. At the start of the business, they invested X 13000 and X 25000, respectively. At the end of 3 yr their total profit was X 76000. What will be share of Q out of this profit ?

Options

A. X 50000
B. X 26000
C. ? 55000
D. ? 21000

Answer

To find the share of Q out of the total profit, we will follow these steps:

### Step 1: Determine the investment ratio of P and Q
P's investment = X 13,000
Q's investment = X 25,000

The investment ratio of P to Q is:
\[ \text{Ratio of P to Q} = \frac{13000}{25000} = \frac{13}{25} \]

### Step 2: Calculate the total parts in the ratio
Total parts in the ratio = 13 + 25 = 38 parts

### Step 3: Calculate Q's share of the profit
Total profit = X 76,000

To find Q's share, we will use the ratio of Q's investment:
\[ \text{Q's share} = \text{Total Profit} \times \frac{\text{Q's investment}}{\text{Total investment}} = 76000 \times \frac{25}{38} \]

### Step 4: Perform the calculation
Calculating Q's share:
\[ \text{Q's share} = 76000 \times \frac{25}{38} \]
\[ = 76000 \times 0.6578947368 \approx 50000 \]

### Conclusion
Q's share out of the total profit is approximately X 50,000.

---