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A and B started a business by investing in the ratio of 2 : 3. After 2 months, C joined them by investing 120% of A’s capital and after 2 more months, D joined them by investing 112.5% of A’s capital. After 6 more months, B withdraws his whole capital. If after 1 year the difference between profit shares of A and B together and that of C and D together is Rs. 7000, then find the total profit.

A and B started a business by investing in the ratio of 2 : 3. After 2 months, C joined them by investing 120% of A’s capital and after 2 more months, D joined them by investing 112.5% of A’s capital. After 6 more months, B withdraws his whole capital. If after 1 year the difference between profit shares of A and B together and that of C and D together is Rs. 7000, then find the total profit. Correct Answer Rs. 56000

Let the capitals of A and B be 2x and 3x respectively.

So, the capital of C = 2x × 120/100 = 12x/5

And the capital of D = 2x × 112.5/100 = 9x/4

Now, the ratio between the profit shares of A, B, C and D:

: : :

24x : 30x : 24x : 18x

4 : 5 : 4 : 3

Again let the profit shares of A, B, C and D be 4y, 5y, 4y and 3y respectively.

According to the question:

(A + B) - (C + D) = 7000

(4y + 5y) - (4y + 3y) = 7000

y = 3500

So, the total profit = (4 + 5 + 4 + 3) × 3500 = Rs. 56000

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