A invest Rs. 6400 and B invest Rs. 7200 in a business. After 4 months, A withdrawal 30% of the initial investment and C join with 40% of initial investment of B. After one year, the total profit is 90000. Find the profit of A and C(in Rs.) approximate?

The correct answer is 44494.

We are given the initial investments and changes in the investments of A, B, and C over a period of one year (12 months). Let's calculate the effective investment of each person for 1 month to determine the ratio of their profits.

Step 1: Calculate the effective investment of A
Initial investment of A = Rs. 6400 for the first 4 months.
After 4 months, A withdraws 30% of his initial investment.
Amount withdrawn by A is:

$30\%\text{ of }6400=\frac{30}{100}\times 6400=1920$
Remaining investment of A for the next 8 months is:

$6400-1920=4480$
Total equivalent 1-month investment for A is:

$(6400\times 4)+(4480\times 8)=25600+35840=61440$

Step 2: Calculate the effective investment of B
B invests Rs. 7200 for the entire 12 months.
Total equivalent 1-month investment for B is:

$7200\times 12=86400$

Step 3: Calculate the effective investment of C
C joins the business after 4 months, which means C invests for the remaining 8 months.
C's investment is 40% of B's initial investment:

$40\%\text{ of }7200=\frac{40}{100}\times 7200=2880$
Total equivalent 1-month investment for C is:

$2880\times 8=23040$

Step 4: Determine the profit sharing ratio
The ratio of profit sharing is the ratio of their equivalent 1-month investments:

$\text{A}:\text{B}:\text{C}=61440:86400:23040$
Dividing each term by 1920 to simplify:

$\text{A}:\text{B}:\text{C}=32:45:12$

Step 5: Calculate the combined profit of A and C
Total sum of the ratio parts is:

$32+45+12=89$
Total profit = Rs. 90000.
The combined share of A and C is:

$\text{Share of A and C}=\frac{32+12}{89}\times 90000$
$=\frac{44}{89}\times 90000$
$=\frac{3960000}{89}\approx 44494.38$
Rounding to the nearest integer, the combined profit of A and C is approximately Rs. 44494.