Partnership Profit Distribution Calculation
This problem requires calculating profit shares based on investment amounts and time duration, a common scenario in partnership business problems.
Calculating Effective Investment
Profit is distributed based on the ratio of 'investment multiplied by time'. The business operates for a year (12 months).
- Partner X: Invested Rs. 50,000 for 12 months. Effective Investment = $50,000 \times 12 = 6,00,000$.
- Partner Y: Invested Rs. 1,00,000 for 12 months. Effective Investment = $1,00,000 \times 12 = 12,00,000$.
- Partner Z: Joined after 6 months, investing Rs. 1,50,000 for the remaining 6 months. Effective Investment = $1,50,000 \times 6 = 9,00,000$.
Determining the Profit Sharing Ratio
The ratio of effective investments determines how the profit is shared.
Ratio (X:Y:Z) = $6,00,000 : 12,00,000 : 9,00,000$.
Simplify the ratio by dividing each part by their greatest common divisor (30,000):
Ratio (X:Y:Z) = $2 : 4 : 3$.
Distributing the Total Profit
The total profit is Rs. 90,000. This is divided according to the ratio 2:4:3.
Total ratio parts = $2 + 4 + 3 = 9$ parts.
Value of 1 part = Total Profit / Total Parts = Rs. $90,000 / 9 = 10,000$.
- X's Profit Share = $2 \text{ parts} \times \text{Rs. } 10,000/\text{part} = \text{Rs. } 20,000$.
- Y's Profit Share = $4 \text{ parts} \times \text{Rs. } 10,000/\text{part} = \text{Rs. } 40,000$.
- Z's Profit Share = $3 \text{ parts} \times \text{Rs. } 10,000/\text{part} = \text{Rs. } 30,000$.
Calculating the Difference in Earnings
The question asks for the difference between Z's earnings and X's earnings.
Difference = Z's Profit Share - X's Profit Share
Difference = Rs. $30,000 - \text{Rs. } 20,000 = \text{Rs. } 10,000$.
Similar Questions
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Important Questions from Partnership
Three partners X, Y and Z started their business by investing ₹40,000, ₹38,000 and ₹30,000, respectively. After 6 months, X and Z made additional investments of ₹20,000 and ₹15,000 respectively, whereas Y withdrew ₹8,000. Find the share of Y (in ₹) in the total profit of ₹38,880 made at the end of the year.
A, B and C invested their capitals in the ratio 2 ∶ 3 ∶ 5. The ratio of months for which they invested is 4 ∶ 2 ∶ 3, respectively. If the difference between the profit shares of A and B is Rs. 1,86,000, then C's share of profit (in Rs.) is:
A started a business with a capital of Rs. 54,000 and admitted B and C after 4 months and 6 months, respectively. At the end of the year, the profit was divided among the three in the ratio 1 ∶ 4 ∶ 5. What is the sum (in Rs.) of the capitals invested by B and C?
A, B and C started a business in partnership. Initially, A invested Rs. 29,000, while B and C invested Rs. 25,000 each. After 4 months, A withdrew Rs. 3,000. After 2 more months, C invested Rs. 12,000 more. Find the share of C( in Rs.) in the profit of Rs. 33,200 at the end of the year.
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)?
