Profit Ratio Calculation Explained
In partnerships, the profit ratio is determined by the product of the capital ratio and the time ratio.
The formula is:
$ \text{Profit Ratio} = \text{Capital Ratio} \times \text{Time Ratio} $
Applying the Formula
Given:
- Capital Ratio of A and B = $3:2$
- Time Ratio of A and B = $2:3$
Step-by-Step Calculation
- Represent the ratios mathematically:
- Capital Ratio = $\frac{3}{2}$
- Time Ratio = $\frac{2}{3}$
- Multiply the capital ratio by the time ratio to find the profit ratio:
$ \text{Profit Ratio (A:B)} = \left( \frac{\text{Capital}_A}{\text{Capital}_B} \right) \times \left( \frac{\text{Time}_A}{\text{Time}_B} \right) $
$ \text{Profit Ratio (A:B)} = \left( \frac{3}{2} \right) \times \left( \frac{2}{3} \right) $
- Perform the multiplication:
$ \text{Profit Ratio (A:B)} = \frac{3 \times 2}{2 \times 3} = \frac{6}{6} $
- Simplify the result:
$ \text{Profit Ratio (A:B)} = \frac{1}{1} = 1:1 $
Therefore, the profit ratio of A and B is $1:1$.
Similar Questions
- In a three-way joint venture, the first investor contributes capital, the second contributes time and strategy, and the third brings a network of suppliers. They agree to share profits in the ratio 3:2:2. If the venture earns Rs. 1,40,000 in the first year, how much should the strategizing (second) partner receive?
- The investments of three partners, P, Q, and R, are initially in the ratio 6 : 7 : 9. After a year, P adds ₹30,000, Q adds ₹25,000, and R adds some amount to their respective investments. The new ratio of their investments becomes 8 : 9 : 11. Find the amount (in ₹) added by partner R.
- A, B, and C invested in a business in the ratio 2:3:5. After a year, the total profit is Rs. 1,00,000. What is B's share?
- A and B invested Rs. 60,000 and Rs. 40,000 respectively for 12 months. A take 10% of the profit for managing. The remaining profit of Rs. 90,000 is divided based on capital. What is B’s share?
- Partners X and Y entered into a business investing Rs. 50,000 and Rs. 1,00,000 respectively. After 6 months, Z joins with Rs. 1,50,000. At year-end, profit was Rs. 90,000. How much more did Z earn than X?
- M and N start a business with Rs. 2,00,000 and Rs. 3,00,000 respectively. After 4 months, M adds Rs. 1,00,000 more, and N withdraws Rs. 50,000. At the end of 1 year, they make a profit of Rs. 1,80,000. What is N's share of profit?
- A, B, and C invest in the ratio 4:5:6. The time ratio is 3:2:1. What is the ratio of their profits?
- A and B started a business by investing Rs. 75,000 and Rs. 45,000 respectively. After 3 months, C joined with Rs. 60,000. At the end of the year, what is C’s share in a profit of Rs. 40,000 (approx.)?
- P starts a business with Rs. 8,000. Q joins after 5 months with Rs. 12,000. If the profit at the end of the year is Rs. 6,800, what is Q’s share (approx.)?
- D and E start a business with equal investments. After 4 months, D adds Rs. 10,000 more. At the end of 1 year, if the total profit is Rs. 33,000, and E's share is Rs. 15,000, what was their initial investment?
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)?
