An entrepreneur, Anita, launched a tech startup with an initial investment of ₹1,00,000. Four months later, standard operation required expansion, and Bhavna joined the venture with a capital of ₹1,20,000. After an additional 4 months had elapsed, Anita decided to pull out ₹40,000 of her initial investment. Find the ratio in which the total profit should be divided between Anita and Bhavna at the conclusion of one year.

The correct option is 13 : 12.

To find the ratio in which the total profit should be divided between Anita and Bhavna at the end of one year (12 months), we need to calculate the ratio of their effective investments over the total period of 12 months.

Step 1: Calculate Anita's total effective investment
Anita initially invested ₹1,00,000.
She kept this initial investment of ₹1,00,000 for the first 8 months (4 months before Bhavna joined + 4 additional months).
After 8 months, she withdrew ₹40,000, leaving her with an investment of:
₹1,00,000 - ₹40,000 = ₹60,000 for the remaining 4 months of the year (12 - 8 = 4 months).

Anita's total effective capital = $(100000\times 8)+(60000\times 4)$

$=800000+240000=1040000$

Step 2: Calculate Bhavna's total effective investment
Bhavna joined 4 months after Anita, which means her capital was invested for the remaining 8 months of the year (12 - 4 = 8 months).
Bhavna invested ₹1,20,000.

Bhavna's total effective capital = $120000\times 8=960000$

Step 3: Find the ratio of their profits
The profit is divided in the ratio of their total effective investments:

Ratio = $1040000:960000$

Dividing both sides by 80,000 gives:

Ratio = $13:12$

Thus, the total profit should be divided between Anita and Bhavna in the ratio 13 : 12.