Understanding the Profit Sharing Scenario
This problem requires calculating the profit share for partner R. We need to consider the initial investment ratios (6 : 3 : 15) and how the investments of partners Q and R changed during the year. The total profit is ₹29900 for a 1-year period (12 months).
Calculating Effective Investments for Profit Ratio
We calculate the effective investment duration for each partner to determine their profit-sharing ratio.
- Partner P: Invested for the full 12 months. Effective Investment = (Share Ratio) \(\times\) (Months) = \(6 \times 12 = 72\).
- Partner Q: Invested for the first 5 months. Then withdrew 80% of his share. This means 20% (\(100\% - 80\%\)) of his share remained active for the rest of the year (\(12 - 5 = 7\) months). Effective Investment = \((3 \times 5) + (3 \times 0.20 \times 7) = 15 + 4.2 = 19.2\).
- Partner R: Withdrew 52% of his share 4 months before the year ended. So, he invested fully for \(12 - 4 = 8\) months. For the remaining 4 months, only 48% (\(100\% - 52\%\)) of his share was active. Effective Investment = \((15 \times 8) + (15 \times 0.48 \times 4) = 120 + 28.8 = 148.8\).
Determining the Profit Ratio
The ratio of effective investments is P : Q : R = 72 : 19.2 : 148.8.
To simplify, multiply by 10 to remove decimals: 720 : 192 : 1488.
Divide by the greatest common divisor or simplify in steps. Dividing by 16: \(720 / 16 = 45\) \(192 / 16 = 12\) \(1488 / 16 = 93\) Ratio becomes 45 : 12 : 93.
Divide by 3: \(45 / 3 = 15\) \(12 / 3 = 4\) \(93 / 3 = 31\) The final profit-sharing ratio is 15 : 4 : 31.
Calculating R's Share of Profit
Total profit = ₹29900.
Sum of ratio parts = \(15 + 4 + 31 = 50\).
R's share is calculated using his portion of the ratio: \( \text{R's Share} = \left( \frac{\text{R's Ratio Part}}{\text{Total Ratio Parts}} \right) \times \text{Total Profit} \) \( \text{R's Share} = \left( \frac{31}{50} \right) \times 29900 \)
\( \text{R's Share} = 31 \times \frac{29900}{50} \) \( \text{R's Share} = 31 \times 598 \) \( \text{R's Share} = 18538 \)
Therefore, R's share in the profit is ₹18538.
Similar Questions
- A and B start a business by investing ₹40,000 and ₹60,000, respectively. At the end of the year, they earn a profit of ₹20,000. How much profit will A receive?
- Two partners M and N buy a car. M pays his share of $\frac{3}{7}$th of the total cost of the car. M pays ₹ 31,540 less than N. What is the cost of the car?
Important Questions from Partnership
A, B and C invest in a business in the ratio 4 ∶ 5 ∶ 7. C is a sleeping partner, so his share of profits will be half of what it would have been if he were a working partner. If they make Rs 36,000 profit of which 25% is reinvested in the business, how much does B get (in Rs)?
Sumit, Ravi and Puneet invest Rs. 45000, Rs. 81000 and Rs. 90000 respectively to start a business. At the end of the year the total profit is Rs. 4800. 30% of the total profit gives in charity and rest is divided among them. What will be the share of Sumit?
A sum of ₹ 159250 is divided among A, B, C, and D such that the ratio of the shares of A and B is 1 : 3, that of B and C is 2 : 5, and that of C and D is 2 : 3. The share (in ₹) of A is:
A and B start a business by investing Rs. 1,00,000 and Rs. 1,50,000 respectively. Find the respective share of each out of a total profit of Rs. 24, 000.
Two partners A and B have started business with the capitals of Rs. 6,000 and Rs. 8,000 respectively. If they made profit of Rs. 5,600 then the share (in Rs.) of A is:
