Three entrepreneurs, Alex, Blake, and Chris, launched a joint venture. Alex invested Rs. 90,000, Blake invested Rs. 60,000, and Chris invested Rs. 70,000. Six months into the business, Alex added an additional Rs. 30,000 to his capital, while Blake withdrew Rs. 20,000.
If the venture generated a total profit of Rs. 3,60,000 at the end of one year, how much will Blake receive as his share?

The correct answer is Rs. 80,000.

To determine Blake's share of the total profit, we calculate the equivalent capital invested by Alex, Blake, and Chris over the 1-year (12-month) period. Equivalent capital is calculated as the product of the amount invested and the duration for which it was invested in months.

1. Alex's Equivalent Capital:
Alex invested Rs. 90,000 for the first 6 months.
After 6 months, he added Rs. 30,000, bringing his investment to Rs. 90,000 + Rs. 30,000 = Rs. 1,20,000 for the remaining 6 months.

$\text{Alex's Equivalent Capital}=(\mathrm{90,000}\times 6)+(\mathrm{1,20,000}\times 6)$

$\text{Alex's Equivalent Capital}=\mathrm{5,40,000}+\mathrm{7,20,000}=\mathrm{12,60,000}$

2. Blake's Equivalent Capital:
Blake invested Rs. 60,000 for the first 6 months.
After 6 months, he withdrew Rs. 20,000, reducing his investment to Rs. 60,000 - Rs. 20,000 = Rs. 40,000 for the remaining 6 months.

$\text{Blake's Equivalent Capital}=(\mathrm{60,000}\times 6)+(\mathrm{40,000}\times 6)$

$\text{Blake's Equivalent Capital}=\mathrm{3,60,000}+\mathrm{2,40,000}=\mathrm{6,00,000}$

3. Chris's Equivalent Capital:
Chris invested Rs. 70,000 without any change for the full 12 months.

$\text{Chris's Equivalent Capital}=\mathrm{70,000}\times 12=\mathrm{8,40,000}$

4. Ratio of Investments:
The ratio of profit distribution among Alex, Blake, and Chris is proportional to their equivalent capital:

$\text{Alex}:\text{Blake}:\text{Chris}=\mathrm{12,60,000}:\mathrm{6,00,000}:\mathrm{8,40,000}$

Dividing each part of the ratio by 60,000 to simplify:

$\text{Ratio}=21:10:14$

$\text{Total Ratio Parts}=21+10+14=45$

5. Calculating Blake's Share of Profit:
Given that the total profit generated at the end of the year is Rs. 3,60,000:

$\text{Blake's Share}=\left(\frac{10}{45}\right)\times \mathrm{3,60,000}$

$\text{Blake's Share}=10\times \mathrm{8,000}=\text{Rs. 80,000}$

Thus, Blake will receive Rs. 80,000 as his share of the profit.