Alex and Blake launch a joint tech venture by contributing $10,000 and $15,000, respectively. After 3 months, Alex reduces his capital by withdrawing 20% of his initial contribution, while Charlie joins the project by investing an amount equal to 40% of Blake's initial contribution. If the enterprise earns a total net profit of $112,000 at the end of one year, what is the combined share of profit earned by Alex and Charlie?

The correct answer is $52,000.

To find the combined share of profit earned by Alex and Charlie, we calculate the equivalent monthly investment (Capital × Time in months) for each partner over the 1-year period (12 months).

1. Alex's Total Investment:
Alex begins with an initial capital of $10,000 for the first 3 months.
After 3 months, he withdraws 20% of his initial contribution:
$\text{Withdrawal}=20\%\times \mathrm{10,000}=\mathrm{2,000}$
His remaining capital for the remaining 9 months is:
$\text{Reduced Capital}=\mathrm{10,000}-\mathrm{2,000}=\mathrm{8,000}$
Total equivalent monthly investment for Alex:
$\text{Alex's Equivalent Capital}=(\mathrm{10,000}\times 3)+(\mathrm{8,000}\times 9)=\mathrm{30,000}+\mathrm{72,000}=\mathrm{102,000}$

2. Blake's Total Investment:
Blake keeps his initial contribution of $15,000 unchanged for the entire 12 months.
Total equivalent monthly investment for Blake:
$\text{Blake's Equivalent Capital}=\mathrm{15,000}\times 12=\mathrm{180,000}$

3. Charlie's Total Investment:
Charlie joins after 3 months, so his investment lasts for 9 months.
His capital contribution is 40% of Blake's initial contribution:
$\text{Charlie's Capital}=40\%\times \mathrm{15,000}=\mathrm{6,000}$
Total equivalent monthly investment for Charlie:
$\text{Charlie's Equivalent Capital}=\mathrm{6,000}\times 9=\mathrm{54,000}$

4. Profit Sharing Ratio:
The ratio of profit distribution among Alex, Blake, and Charlie is proportional to their total equivalent investments:
$\text{Alex}:\text{Blake}:\text{Charlie}=\mathrm{102,000}:\mathrm{180,000}:\mathrm{54,000}$
Dividing all terms by 6,000 simplifies the ratio to:
$\text{Ratio}=17:30:9$
Total ratio parts:
$\text{Total Parts}=17+30+9=56$

5. Combined Profit Share of Alex and Charlie:
The enterprise earned a total net profit of $112,000.
The combined ratio parts belonging to Alex and Charlie are:
$\text{Combined Parts}=17+9=26$
Therefore, their combined profit share is:
$\text{Combined Share}=\frac{26}{56}\times \mathrm{112,000}=26\times \mathrm{2,000}=\mathrm{52,000}$

The combined share of profit earned by Alex and Charlie is $52,000.