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Three persons A, B and C invest capital ...

Three persons A, B and C invest capital in the ratio `5:4:8`. After 2 months A withdraws `20%` of his investment. One month later B increases his investment by `75%`. Further, 2 months later, C makes an additional investment of `25%` of his initial investment. At the end of the year if the difference in profit shares of A and B is ₹7500, how much does C’s profit share exceed that of B ?

A

₹10000

B

₹10500

C

₹12,000

D

₹12,500

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we will follow the investments of A, B, and C, calculate their total contributions, and then determine the profit shares. ### Step 1: Determine Initial Investments The initial investments of A, B, and C are in the ratio of 5:4:8. Let's assume a common multiplier \( x \). - A's investment = \( 5x \) - B's investment = \( 4x \) - C's investment = \( 8x \) ### Step 2: Calculate A's Investment After 2 Months A withdraws 20% of his investment after 2 months. - Initial investment of A = \( 5x \) - Amount withdrawn = \( 20\% \) of \( 5x = 0.2 \times 5x = x \) - Remaining investment = \( 5x - x = 4x \) ### Step 3: Calculate Total Investment of A A's investment lasts for 2 months at \( 5x \) and for the remaining 10 months at \( 4x \). - Total contribution of A = \( 5x \times 2 + 4x \times 10 = 10x + 40x = 50x \) ### Step 4: Calculate B's Investment After 3 Months B increases his investment by 75% after 3 months. - Initial investment of B = \( 4x \) - Increased investment = \( 4x + 75\% \text{ of } 4x = 4x + 3x = 7x \) ### Step 5: Calculate Total Investment of B B's investment lasts for 3 months at \( 4x \) and for the remaining 9 months at \( 7x \). - Total contribution of B = \( 4x \times 3 + 7x \times 9 = 12x + 63x = 75x \) ### Step 6: Calculate C's Investment After 5 Months C makes an additional investment of 25% of his initial investment after 5 months. - Initial investment of C = \( 8x \) - Additional investment = \( 25\% \text{ of } 8x = 2x \) - New total investment = \( 8x + 2x = 10x \) ### Step 7: Calculate Total Investment of C C's investment lasts for 5 months at \( 8x \) and for the remaining 7 months at \( 10x \). - Total contribution of C = \( 8x \times 5 + 10x \times 7 = 40x + 70x = 110x \) ### Step 8: Calculate Total Investment Now, we can sum up the total investments of A, B, and C. - Total investment = \( 50x + 75x + 110x = 235x \) ### Step 9: Determine Profit Shares The profit shares are proportional to their total investments. - A's share = \( \frac{50x}{235x} \) - B's share = \( \frac{75x}{235x} \) - C's share = \( \frac{110x}{235x} \) ### Step 10: Calculate the Difference in Profit Shares We know that the difference in profit shares between A and B is ₹7500. - Difference = \( \frac{75x}{235x} - \frac{50x}{235x} = \frac{25x}{235x} \) - Given that this difference equals ₹7500, we can set up the equation: \[ \frac{25x}{235} = 7500 \] ### Step 11: Solve for x To find \( x \): \[ 25x = 7500 \times 235 \] \[ x = \frac{7500 \times 235}{25} = 70500 \] ### Step 12: Calculate Profit Shares Now, we can calculate the profit shares: - A's profit = \( \frac{50}{235} \times 70500 = 15000 \) - B's profit = \( \frac{75}{235} \times 70500 = 22500 \) - C's profit = \( \frac{110}{235} \times 70500 = 33000 \) ### Step 13: Determine the Difference Between C's and B's Profit Shares Finally, we find how much C’s profit share exceeds that of B: \[ C's profit - B's profit = 33000 - 22500 = 10500 \] ### Final Answer C's profit share exceeds that of B by ₹10,500. ---
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