Partnership Profit Share Calculation
This problem involves calculating the share of profit for a partner (Q) in a business, considering their investment amount and the duration they were part of the business.
Investment-Time Products
Profit is distributed based on the ratio of investment multiplied by the time duration each partner invested.
- P's Investment: Rs. 8,000 for 12 months (full year). P's investment-time product = $8,000 \times 12 = 96,000$.
- Q's Investment: Rs. 12,000. Q joined after 5 months, so Q invested for $12 - 5 = 7$ months. Q's investment-time product = $12,000 \times 7 = 84,000$.
Profit Ratio Calculation
The ratio of profit sharing between P and Q is the ratio of their investment-time products:
Ratio P : Q = $96,000 : 84,000$
Simplify the ratio by dividing both sides by their greatest common divisor (12,000):
Ratio P : Q = $8 : 7$
The total parts in the ratio are $8 + 7 = 15$.
Q's Profit Share
The total profit is Rs. 6,800. Q's share is calculated based on their ratio part (7) out of the total parts (15).
Q's Share = $\frac{\text{Q's Ratio Part}}{\text{Total Ratio Parts}} \times \text{Total Profit}$
Q's Share = $\frac{7}{15} \times 6,800$
Q's Share = $\frac{47,600}{15}$
Q's Share $\approx 3,173.33$
Therefore, Q's approximate share of the profit is Rs. 3,173.33.
