R and S are partners sharing profits in the ratio of 5 : 3. T joins the firm as a new partner. R given $${\frac{1}{4}^{{\text{th}}}}$$ of his share and S given $${\frac{2}{5}^{{\text{th}}}}$$ of his share to new partner. New profit sharing ratio of R, S and T will be

Here's how to find the new profit sharing ratio of R, S, and T:

1. Initial Profit Sharing Ratio:

R:S = 5:3
2. Share Given to New Partner:

R gives 1/4 of his share: 5 * (1/4) = 5/4
S gives 2/5 of his share: 3 * (2/5) = 6/5
3. Updated Share for Existing Partners:

R's updated share: 5 - 5/4 = 15/4
S's updated share: 3 - 6/5 = 9/5
4. Total Share After T Joins:

Combined share given to T: 5/4 + 6/5 = 49/20
Total share after T joins: (15/4) + (9/5) + (49/20) = 160/20
5. New Profit Sharing Ratio:

R's new ratio: (15/4) / (160/20) = 15/32
S's new ratio: (9/5) / (160/20) = 9/40
T's new ratio: (49/20) / (160/20) = 49/160
Therefore, the new profit sharing ratio for R, S, and T is 75:36:49.

I hope this explanation is clear and helpful! Let me know if you have any further questions.