P starts a business with a capital of Rs. 5000 . After 3 months , Q joins with a capital of Rs. 6000 and 5 mon

Question

P starts a business with a capital of Rs. 5000 . After 3 months , Q joins with a capital of Rs. 6000 and 5 months from the start, R invests Rs. 8000 . If the total profit at the end of the year is Rs. 3400 , calculate the amount that each will receive.

Accepted Answer

The business operated for a full year (

12 months

). Let us determine the individual holding periods for each investor:
* P's duration =

12 months

(from inception)
* Q's duration =

12 - 3 = 9 months

* R's duration =

12 - 5 = 7 months

Now, compute the ratio of their net equivalent monthly capitals:

P : Q : R = (5000 \times 12) : (6000 \times 9) : (8000 \times 7)

P : Q : R = 60000 : 54000 : 56000 = 60 : 54 : 56 = 30 : 27 : 28

Sum of the ratio values:

30 + 27 + 28 = 85

Total profit earned =

Rs. 3400

P's profit allocation:

Profit of P = \frac{30}{85} \times 3400 = 30 \times 40 = Rs. 1200

Q's profit allocation:

Profit of Q = \frac{27}{85} \times 3400 = 27 \times 40 = Rs. 1080

R's profit allocation:

Profit of R = \frac{28}{85} \times 3400 = 28 \times 40 = Rs. 1120

P starts a business with a capital of $Rs. 5000$ . After $3 months$ , Q joins with a capital of $Rs. 6000$ and $5 months$ from the start, R invests $Rs. 8000$ . If the total profit at the end of the year is $Rs. 3400$ , calculate the amount that each will receive.

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P starts a business with a capital of Rs. 5000. After 3 months, Q joins with a capital of Rs. 6000 and 5 months from the start, R invests Rs. 8000. If the total profit at the end of the year is Rs. 3400, calculate the amount that each will receive.