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A and B started a business together and ...

A and B started a business together and the respective ratio between the investments of A and B was 5:9. After 4 months from the start of business, C joined and the respective ratio between the investments of B and C was 3 :7. If the annual profit earned by them was Rs 7,560, what is C’s share in the profit' ? (In Rs)

A

Rs 3780

B

Rs 3627

C

Rs 3572

D

Rs 3667

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we will follow the given information and calculate C's share in the profit. ### Step 1: Determine the Investments of A, B, and C The investment ratio of A and B is given as 5:9. Let's denote: - Investment of A = 5x - Investment of B = 9x Next, we know that the investment ratio of B and C is 3:7. We can express C's investment in terms of B's investment: - Investment of B = 9x - Investment of C = (7/3) * Investment of B = (7/3) * 9x = 21x Now we have: - Investment of A = 5x - Investment of B = 9x - Investment of C = 21x ### Step 2: Calculate the Time of Investment - A and B invested for 12 months. - C joined after 4 months, so C invested for 8 months. ### Step 3: Calculate the Effective Investment The profit-sharing ratio is based on the effective investment, which is calculated as: - Effective investment of A = Investment of A * Time = 5x * 12 = 60x - Effective investment of B = Investment of B * Time = 9x * 12 = 108x - Effective investment of C = Investment of C * Time = 21x * 8 = 168x ### Step 4: Determine the Total Effective Investment Now, we can find the total effective investment: - Total effective investment = Effective investment of A + Effective investment of B + Effective investment of C - Total effective investment = 60x + 108x + 168x = 336x ### Step 5: Calculate the Profit Share The total profit earned is Rs 7,560. To find the value of 'x': - Total profit = Rs 7,560 - Therefore, the value of 1x = Total profit / Total effective investment = 7560 / 336 = 22.5 ### Step 6: Calculate C's Share in the Profit C's effective investment is 168x. Thus, C's share in the profit is: - C's share = Effective investment of C * Value of x = 168x * 22.5 = 3780 ### Final Answer C’s share in the profit is Rs 3,780. ---
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