A, B, and C invest in a business in the ratio 2:3:5. After 4 months, A increases his capital by 50%. B decreases his capital by \(\frac{1}{3}\), and C leaves the capital unchanged. At the end of the year, if the total profit is Rs. 33,000, find the share of B.
Rs. 7,700
To solve this problem, we need to determine the share of B from the total profit of Rs. 33,000. The investment scenario changes partway through the year, so we need to calculate the effective investment for each person considering the changes.
- Initially, A, B, and C invest in the ratio 2:3:5. Let's assume their investments are 2x, 3x, and 5x, respectively.
- These amounts are invested for 12 months, but changes occur after 4 months:
- A increases his capital by 50%: Current investment = \( 2x + 0.5 \cdot 2x = 3x \). So, A invests 2x for 4 months and 3x for 8 months.
- B decreases his capital by \(\frac{1}{3}\): Current investment = \( 3x \cdot \left(1 - \frac{1}{3}\right) = 2x \). So, B invests 3x for 4 months and 2x for 8 months.
- C maintains his investment unchanged at 5x: Invests 5x for entire 12 months.
- Calculate the total effective investments over the year for A, B, and C:
- Total investment by A = \( (2x \times 4) + (3x \times 8) = 8x + 24x = 32x \)
- Total investment by B = \( (3x \times 4) + (2x \times 8) = 12x + 16x = 28x \)
- Total investment by C = \( 5x \times 12 = 60x \)
- Find the total ratio of investments: \( A:B:C = 32x:28x:60x = 16:14:30 \).
- Simplify the ratio by dividing by 2: \( 16:14:30 = 8:7:15 \).
- The total profit is Rs. 33,000. B's share of the profit is calculated as follows:
- Total parts = \( 8 + 7 + 15 = 30 \) parts.
- B's share of profit = \( \frac{7}{30} \) part of Rs. 33,000.
- B's profit = \( \frac{7}{30} \times 33,000 = 7,700 \).
Therefore, the share of B from the profit is Rs. 7,700.
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?
- If the ratio of capital of A and B is 3:2 and the time for which they invested is in the ratio 2:3, then the profit ratio is:
- 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.)?
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)?
