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A, B and C invested in a business in the...

A, B and C invested in a business in the ratio of 6 : 8 : 9. B invested for period whose numerical value is `112.5%` of ratio of B’s investment but A and C invested for one year. If the profit of B at the end of the year Is ₹16750 then what is the share of the profit of C?

A

₹20225

B

₹22125

C

₹25225

D

₹25125

Text Solution

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The correct Answer is:
To solve the problem step by step, let's break it down: ### Step 1: Understand the Investment Ratios The investments of A, B, and C are in the ratio of 6:8:9. We can represent their investments as: - A's investment = 6X - B's investment = 8X - C's investment = 9X ### Step 2: Determine the Time of Investment A and C invested for 1 year (12 months). B invested for a period that is 112.5% of the ratio of B's investment. To find the time B invested: - B's investment ratio = 8 - 112.5% of 8 = (112.5/100) * 8 = 9 months ### Step 3: Calculate the Effective Investment The profit is distributed based on the product of investment and time. - A's effective investment = 6X * 12 months = 72X - B's effective investment = 8X * 9 months = 72X - C's effective investment = 9X * 12 months = 108X ### Step 4: Calculate the Total Effective Investment Now, we can find the total effective investment: Total = A's effective investment + B's effective investment + C's effective investment Total = 72X + 72X + 108X = 252X ### Step 5: Determine the Profit Share of B We know that B's profit at the end of the year is ₹16,750. Since B's effective investment is 72X, we can set up the equation: - Profit share of B = (B's effective investment / Total effective investment) * Total Profit - 16,750 = (72X / 252X) * Total Profit ### Step 6: Calculate the Total Profit From the equation above, we can find the total profit: Total Profit = 16,750 * (252X / 72X) = 16,750 * 3.5 = ₹58,625 ### Step 7: Calculate C's Profit Share Now, we can calculate C's profit share: - C's profit = (C's effective investment / Total effective investment) * Total Profit - C's profit = (108X / 252X) * 58,625 ### Step 8: Simplify the Calculation C's profit = (108 / 252) * 58,625 C's profit = (9 / 21) * 58,625 C's profit = (3 / 7) * 58,625 Calculating this gives: C's profit = 25,125 ### Final Answer C's share of the profit is ₹25,125. ---
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