# 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

A. 15 : 01 : 26

B. 75 : 36 : 49

C. 25 : 15 : 26

D. 20 : 9 : 11

**Answer: Option B **

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.