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Three persons A, B and C started a busin...

Three persons A, B and C started a business with their shares in the ratio 3 : 4: 5. After 4 months B withdrew his 50% share and C withdrew his 20% share 4 months prior to completion of the year. If total profit in the year is ₹ 31,000 then find the share of A in the profit.

A

₹7750

B

₹9000

C

₹9300

D

₹10330

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to determine the share of person A in the total profit of ₹31,000 based on their investment and the time for which they invested. Let's break it down step by step. ### Step 1: Determine the Initial Investment Shares The initial investment ratio of A, B, and C is given as: - A : B : C = 3 : 4 : 5 Let's denote their investments as: - A's investment = 3x - B's investment = 4x - C's investment = 5x ### Step 2: Calculate the Time Each Person Invested - A invests for the entire year (12 months). - B invests for the first 4 months at full investment (4x), and then withdraws 50% of his share, leaving him with 2x for the remaining 8 months. - C invests for the first 8 months at full investment (5x), and then withdraws 20% of his share, leaving him with 4x for the last 4 months. ### Step 3: Calculate the Effective Investment of Each Person Now we calculate the effective investment for each person, which is the product of their investment and the time they invested. - **A's effective investment**: \[ = 3x \times 12 = 36x \] - **B's effective investment**: \[ = (4x \times 4) + (2x \times 8) = 16x + 16x = 32x \] - **C's effective investment**: \[ = (5x \times 8) + (4x \times 4) = 40x + 16x = 56x \] ### Step 4: Total Effective Investment Now we sum up the effective investments: \[ \text{Total effective investment} = 36x + 32x + 56x = 124x \] ### Step 5: Determine the Profit Sharing Ratio The profit-sharing ratio is based on their effective investments: - A : B : C = 36x : 32x : 56x - Simplifying this ratio: \[ = 36 : 32 : 56 \] Dividing each term by 4: \[ = 9 : 8 : 14 \] ### Step 6: Calculate A's Share of the Profit The total profit is ₹31,000. The total parts in the profit-sharing ratio are: \[ 9 + 8 + 14 = 31 \] Now, we can find the value of one part: \[ \text{Value of one part} = \frac{31,000}{31} = 1,000 \] A's share of the profit: \[ \text{A's share} = 9 \times 1,000 = 9,000 \] ### Final Answer Thus, A's share in the profit is **₹9,000**. ---
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