Arthur, Bianca, and Cyrus enter into a joint business venture. Arthur invests $60,000, Bianca invests $40,000, and Cyrus invests $30,000. After 3 months, Bianca increases her investment by 25%, while Cyrus reduces his investment by 20%. If the total profit earned at the end of 1 year is $133,000, what is Cyrus’s share of the profit?

The correct option is $25,500.

To find Cyrus’s share of the total profit, we calculate the effective investment (investment multiplied by duration in months) for each partner over the 1-year (12 months) period.

Step 1: Calculate Arthur's total investment-months

Arthur invests $60,000 for the entire duration of 12 months without making any changes.

$\text{Arthur's investment}=60000\times 12=720000$

Step 2: Calculate Bianca's total investment-months

For the first 3 months, Bianca invests $40,000.
After 3 months, she increases her investment by 25%:

$\text{Increase}=25\%\text{of}40000=\frac{25}{100}\times 40000=10000$

Her new investment for the remaining 9 months is:

$\text{New investment}=40000+10000=50000$

Total investment-months for Bianca:

$\text{Bianca's investment}=(40000\times 3)+(50000\times 9)=120000+450000=570000$

Step 3: Calculate Cyrus's total investment-months

For the first 3 months, Cyrus invests $30,000.
After 3 months, he reduces his investment by 20%:

$\text{Reduction}=20\%\text{of}30000=\frac{20}{100}\times 30000=6000$

His new investment for the remaining 9 months is:

$\text{New investment}=30000-6000=24000$

Total investment-months for Cyrus:

$\text{Cyrus's investment}=(30000\times 3)+(24000\times 9)=90000+216000=306000$

Step 4: Determine the ratio of profit shares

The ratio of profit share among Arthur, Bianca, and Cyrus is:

$\text{Ratio}=720000:570000:306000$

Simplifying the ratio by dividing each term by 6,000:

$\text{Ratio}=120:95:51$

Sum of the ratio terms:

$\text{Total ratio parts}=120+95+51=266$

Step 5: Calculate Cyrus's share of the profit

Given total profit = $133,000:

$\text{Cyrus's share}=\frac{51}{266}\times 133000$

Dividing 133,000 by 266 gives 500:

$\text{Cyrus's share}=51\times 500=25500$

Thus, Cyrus’s share of the profit is $25,500.