Ananya and Anjali started a business by investing money in the ratio 3:4 respectively. After some months Aditi joined the business by investing half the amount as Ananya. What percentage of the total profit will Aditi earn?

This is a compound partnership.

The profit between partners is divided in the ratio of their respective weighted investments.

Weighted ratio of investment = (Amount of Investment) * (Number of months invested)

Weighted investment of Ananya = 6x*12 = 72x

Weighted investment of Anjali = 8x*12 = 96x

Weighted investment of Aditi = 3x*(12-y)

Now as we do not know after how many months Aditi we cannot exactly determined her profit share. Hence the answer to this question cannot be determined.