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A and B started a business with different investments. At the start of 2nd, 3rd and 4th quarter each, A and B invested additional amounts of 300 and 200 respectively and in the 4th quarter, amounts invested by them became equal. If annual profit was divided in the ratio of 5: 6 respectively, what was the investment with which A started the business?
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A and B started a business with different investments. At the start of...
Explanation:
Let the initial investment of A be x and that of B be y.
At the start of 2nd quarter, A invested an additional amount of 300. Therefore, his investment at the start of 2nd quarter was x + 300. Similarly, B invested an additional amount of 200, so his investment at the start of 2nd quarter was y + 200.
Similarly, at the start of 3rd quarter, A invested an additional amount of 300, so his investment at the start of 3rd quarter was x + 600. Similarly, B invested an additional amount of 200, so his investment at the start of 3rd quarter was y + 400.
Similarly, at the start of 4th quarter, A invested an additional amount of 300, so his investment at the start of 4th quarter was x + 900. Similarly, B invested an additional amount of 200, so his investment at the start of 4th quarter was y + 600.
Given that the amounts invested by A and B in the 4th quarter became equal. Therefore,
x + 900 = y + 600
x - y = -300
Calculation of Profit:
Let the total profit be P. Then A's share of profit = 5P/11 and B's share of profit = 6P/11.
Let the profit in the 1st quarter be x1, that in the 2nd quarter be x2, that in the 3rd quarter be x3, and that in the 4th quarter be x4.
Total profit P = x1 + x2 + x3 + x4.
A's share of profit = (x1 + x2 + x3 + x4) * 5 / 11.
B's share of profit = (x1 + x2 + x3 + x4) * 6 / 11.
Calculation of A's Initial Investment:
Let's consider the profit earned in each quarter.
In the 1st quarter, A and B's investments were x and y respectively. So, the profit earned in the 1st quarter was proportional to their investments, i.e., x1 / y1 = x / y.
In the 2nd quarter, A and B's investments were x + 300 and y + 200 respectively. So, the profit earned in the 2nd quarter was proportional to their investments, i.e., x2 / y2 = (x + 300) / (y + 200).
In the 3rd quarter, A and B's investments were x + 600 and y + 400 respectively. So, the profit earned in the 3rd quarter was proportional to their investments, i.e., x3 / y3 = (x + 600) / (y + 400).
In the 4th quarter, A and B's investments were x + 900 and y + 600 respectively. Given that the amounts invested by A and B in the 4th quarter became equal, we can write x + 900 = y + 600. Solving this equation, we get x - y = -300. So, A's investment at the start of the business was x = y - 300.
Final Answer:
Therefore
Let the initial investment of A be x and that of B be y.
At the start of 2nd quarter, A invested an additional amount of 300. Therefore, his investment at the start of 2nd quarter was x + 300. Similarly, B invested an additional amount of 200, so his investment at the start of 2nd quarter was y + 200.
Similarly, at the start of 3rd quarter, A invested an additional amount of 300, so his investment at the start of 3rd quarter was x + 600. Similarly, B invested an additional amount of 200, so his investment at the start of 3rd quarter was y + 400.
Similarly, at the start of 4th quarter, A invested an additional amount of 300, so his investment at the start of 4th quarter was x + 900. Similarly, B invested an additional amount of 200, so his investment at the start of 4th quarter was y + 600.
Given that the amounts invested by A and B in the 4th quarter became equal. Therefore,
x + 900 = y + 600
x - y = -300
Calculation of Profit:
Let the total profit be P. Then A's share of profit = 5P/11 and B's share of profit = 6P/11.
Let the profit in the 1st quarter be x1, that in the 2nd quarter be x2, that in the 3rd quarter be x3, and that in the 4th quarter be x4.
Total profit P = x1 + x2 + x3 + x4.
A's share of profit = (x1 + x2 + x3 + x4) * 5 / 11.
B's share of profit = (x1 + x2 + x3 + x4) * 6 / 11.
Calculation of A's Initial Investment:
Let's consider the profit earned in each quarter.
In the 1st quarter, A and B's investments were x and y respectively. So, the profit earned in the 1st quarter was proportional to their investments, i.e., x1 / y1 = x / y.
In the 2nd quarter, A and B's investments were x + 300 and y + 200 respectively. So, the profit earned in the 2nd quarter was proportional to their investments, i.e., x2 / y2 = (x + 300) / (y + 200).
In the 3rd quarter, A and B's investments were x + 600 and y + 400 respectively. So, the profit earned in the 3rd quarter was proportional to their investments, i.e., x3 / y3 = (x + 600) / (y + 400).
In the 4th quarter, A and B's investments were x + 900 and y + 600 respectively. Given that the amounts invested by A and B in the 4th quarter became equal, we can write x + 900 = y + 600. Solving this equation, we get x - y = -300. So, A's investment at the start of the business was x = y - 300.
Final Answer:
Therefore
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A and B started a business with different investments. At the start of 2nd, 3rd and 4th quarter each, A and B invested additional amounts of 300 and 200 respectively and in the 4th quarter, amounts invested by them became equal. If annual profit was divided in the ratio of 5: 6 respectively, what was the investment with which A started the business?
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A and B started a business with different investments. At the start of 2nd, 3rd and 4th quarter each, A and B invested additional amounts of 300 and 200 respectively and in the 4th quarter, amounts invested by them became equal. If annual profit was divided in the ratio of 5: 6 respectively, what was the investment with which A started the business? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A and B started a business with different investments. At the start of 2nd, 3rd and 4th quarter each, A and B invested additional amounts of 300 and 200 respectively and in the 4th quarter, amounts invested by them became equal. If annual profit was divided in the ratio of 5: 6 respectively, what was the investment with which A started the business? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A and B started a business with different investments. At the start of 2nd, 3rd and 4th quarter each, A and B invested additional amounts of 300 and 200 respectively and in the 4th quarter, amounts invested by them became equal. If annual profit was divided in the ratio of 5: 6 respectively, what was the investment with which A started the business?.
A and B started a business with different investments. At the start of 2nd, 3rd and 4th quarter each, A and B invested additional amounts of 300 and 200 respectively and in the 4th quarter, amounts invested by them became equal. If annual profit was divided in the ratio of 5: 6 respectively, what was the investment with which A started the business? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A and B started a business with different investments. At the start of 2nd, 3rd and 4th quarter each, A and B invested additional amounts of 300 and 200 respectively and in the 4th quarter, amounts invested by them became equal. If annual profit was divided in the ratio of 5: 6 respectively, what was the investment with which A started the business? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A and B started a business with different investments. At the start of 2nd, 3rd and 4th quarter each, A and B invested additional amounts of 300 and 200 respectively and in the 4th quarter, amounts invested by them became equal. If annual profit was divided in the ratio of 5: 6 respectively, what was the investment with which A started the business?.
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