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A and B invested in the ratio 4:5. A left after 9 months and B increased by 20 % and C joined with an investment of 33.33% of the present investment of B. The annual profit was 42000. Find the percentage difference between A and B to that of A.

Question

A and B invested in the ratio 4:5. A left after 9 months and B increased by 20 % and C joined with an investment of 33.33% of the present investment of B. The annual profit was 42000. Find the percentage difference between A and B to that of A.

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Solution

Let's break down the problem step by step:

Step 1: Let's assume the initial investment of A and B as 4x and 5x respectively.

Step 2: A left after 9 months, so his investment was for 9 months.

Step 3: B increased his investment by 20%, so his new investment is 5x * 1.2 = 6x.

Step 4: C joined with an investment of 33.33% of the present investment of B, so C's investment is 6x * 0.3333 = 2x.

Step 5: The total investment for the year is: A's investment for 9 months = 4x * 9 = 36x B's investment for 12 months = 6x * 12 = 72x C's investment for 12 months = 2x * 12 = 24x Total investment = 36x + 72x + 24x = 132x

Step 6: The annual profit was 42000. So, the value of x = 42000 / 132 = 318.18

Step 7: The initial investment of A = 4x = 4 * 318.18 = 1272.72 The initial investment of B = 5x = 5 * 318.18 = 1590.9

Step 8: The percentage difference between A and B to that of A = ((1590.9 - 1272.72) / 1272.72) * 100 = 25%

So, the percentage difference between A and B to that of A is 25%.

This problem has been solved

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