Two partners, Alex and Ben, launch a startup enterprise. Alex contributes 3 times as much initial capital as Ben. Following a period of 7 months, Alex pulls out one-third of his invested amount, whereas Ben decides to double his investment. If the venture operates for a total timeframe of 12 months and yields a net profit of ₹60,000, what will be Ben's portion of the profit?

Correct Option: ₹21,250

Step-by-Step Explanation:

To find Ben's portion of the net profit, we need to determine the ratio of total investments made by Alex and Ben over the 12-month period.

Step 1: Define initial investments

Let Ben's initial capital be $x$.

Since Alex contributes 3 times as much capital as Ben, Alex's initial capital is $3x$.

Step 2: Calculate the effective investment for the first 7 months

For the first 7 months, their investments remain unchanged:

Alex's investment for 7 months = $3x\times 7=21x$

Ben's investment for 7 months = $x\times 7=7x$

Step 3: Calculate the effective investment for the remaining 5 months

The total duration of the business is 12 months, so the remaining duration is $12-7=5$ months.

After 7 months:

Alex pulls out one-third of his invested amount:

$\text{Alex's new investment}=3x-\left(\frac{1}{3}\times 3x\right)=3x-x=2x$

Alex's investment for the remaining 5 months = $2x\times 5=10x$

Ben decides to double his investment:

$\text{Ben's new investment}=2\times x=2x$

Ben's investment for the remaining 5 months = $2x\times 5=10x$

Step 4: Calculate total equivalent monthly investment for each partner

Total equivalent investment of Alex = $21x+10x=31x$

Total equivalent investment of Ben = $7x+10x=17x$

Step 5: Determine profit sharing ratio

The ratio of Alex's profit share to Ben's profit share is:

$\text{Alex}:\text{Ben}=31x:17x=31:17$

Step 6: Calculate Ben's share of the net profit

Total profit = ₹60,000

Sum of ratio parts = $31+17=48$

Ben's share = $\left(\frac{17}{48}\right)\times \mathrm{60,000}$

Ben's share = $17\times 1250=\mathrm{21,250}$

Thus, Ben's portion of the profit is ₹21,250.