Question

On 1-4-2022 Sahil and Charu entered into a partnership for sharing profits in the ratio of 4 : 3. They admitted Tanu as a new partner on 1-4-2024 for `1/5`th share which she acquired equally from Sahil and Charu. Sahil, Charu, and Tanu earned profits at a higher rate than the normal rate of return for the year ended 31-3-2025. Therefore, they decided to expand their business. To meet the requirements of additional capital they admitted Puneet as a new partner on 1-4-2025 for `1/7`th share in profits, which he acquired from Sahil and Charu in 7 : 3 ratio.

Calculate:

1. New profit sharing ratio of Sahil, Charu and Tanu for the year 2024-25.
2. New profit sharing ratio of Sahil, Charu, Tanu and Puneet on Puneet’s admission.

Answer 1

(i) Calculation of New Profit Sharing Ratio of Sahil, Charu and Tanu:

Share of Profit given to Tanu \[= \frac{1}{5}\]

Share acquired by Tanu from Sahil $= \frac{1}{2} \text{ of } \frac{1}{5} = \frac{1}{10}$

Share acquired by Tanu from Charu $= \frac{1}{2} \text{ of } \frac{1}{5} = \frac{1}{10}$

Hence, Sahil’s new share $= \frac{4}{7} - \frac{1}{10} = \frac{40 - 7}{70} = \frac{33}{70}$

Charu's new share $= \frac{3}{7} - \frac{1}{10} = \frac{30 - 7}{70} = \frac{23}{70}$

Tanu's new share $= \frac{1}{10} + \frac{1}{10} = \frac{2}{10}$

Thus, New Profit Sharing Ratio among Sahil, Charu and Tanu will be
$$\frac{33}{70} : \frac{23}{70} : \frac{2}{10} \text{ or } \frac{33 : 23 : 14}{70} \text{ or } 33 : 23 : 14$$

(ii) Calculation of New Profit Sharing Ratio of Sahil, Charu, Tanu and Puneet:

Share of Profit given to Puneet $= \frac{1}{7}$

Share acquired by Puneet from Sahil $= \frac{7}{10} \text{ of } \frac{1}{7} = \frac{7}{70}$

Share acquired by Puneet from Charu $= \frac{3}{10} \text{ of } \frac{1}{7} = \frac{3}{70}$

Hence, Sahil’s new share $= \frac{33}{70} - \frac{7}{70} = \frac{26}{70}$

Charu's new share $= \frac{23}{70} - \frac{3}{70} = \frac{20}{70}$

Tanu's share $= \frac{14}{70}$

Puneet's share $= \frac{1}{7}$

Thus, New Profit Sharing Ratio among Sahil, Charu, Tanu, and Puneet:

$$\frac{26}{70} : \frac{20}{70} : \frac{14}{70} : \frac{1}{7} \text{ or } \frac{26 : 20 : 14 : 10}{70} \text{ or } 26 : 20 : 14 : 10 = 13 : 10 : 7 : 5$$