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A started a business with an investment ...

A started a business with an investment of Rs 16000. After 2 months B also became his partner and invested `(3/5)^(th)` of the amount invested by A. Again after 2 more months C entered into the partnership with Rs 8000. After 10 months they had a profit of Rs 6230. Find the share of B in the profit.

A

Rs 1760

B

Rs 1670

C

Rs1780

D

Rs 1680

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we will calculate the share of B in the profit based on the investments and the time each partner invested in the business. ### Step 1: Calculate the investment of B A's investment = Rs 16,000 B's investment = (3/5) * A's investment B's investment = (3/5) * 16,000 = Rs 9,600 **Hint:** To find B's investment, multiply A's investment by 3/5. ### Step 2: Identify the investment of C C's investment = Rs 8,000 **Hint:** C's investment is given directly in the problem. ### Step 3: Determine the time each partner invested - A invested for 10 months (from the start). - B invested for 8 months (joined after 2 months). - C invested for 6 months (joined after 4 months). **Hint:** Calculate the time each partner invested based on when they joined the business. ### Step 4: Calculate the effective capital contribution for each partner - A's contribution = Investment * Time = 16,000 * 10 = Rs 160,000 - B's contribution = Investment * Time = 9,600 * 8 = Rs 76,800 - C's contribution = Investment * Time = 8,000 * 6 = Rs 48,000 **Hint:** Multiply each partner's investment by the number of months they invested. ### Step 5: Find the total capital contribution Total capital contribution = A's contribution + B's contribution + C's contribution Total = 160,000 + 76,800 + 48,000 = Rs 284,800 **Hint:** Add the contributions of all partners to find the total. ### Step 6: Calculate the profit-sharing ratio The profit-sharing ratio is based on their effective contributions: - A's ratio = 160,000 / 284,800 - B's ratio = 76,800 / 284,800 - C's ratio = 48,000 / 284,800 **Hint:** Divide each partner's contribution by the total contribution to find their ratio. ### Step 7: Simplify the ratios To simplify: - A's ratio = 160,000 / 284,800 = 50 / 89 - B's ratio = 76,800 / 284,800 = 24 / 89 - C's ratio = 48,000 / 284,800 = 15 / 89 **Hint:** Simplifying the fractions helps in understanding the share of profit. ### Step 8: Calculate each partner's share of the profit Total profit = Rs 6,230 B's share of profit = (B's ratio) * Total profit B's share = (24/89) * 6,230 **Hint:** Multiply B's ratio by the total profit to find B's share. ### Step 9: Calculate B's share of the profit B's share = (24/89) * 6,230 = Rs 1,680 **Hint:** Perform the multiplication carefully to find the exact amount. ### Final Answer B's share in the profit is Rs 1,680.
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