Bharat and Buhushan are partners in a firm sharing profits and losses in the ratio of 5 : 3. They admit Bhagat for 1/5th share in profits. Calculate the new profit-sharing ratio of the partners when:
(i) Bhagat gets his share equally from the old partners,
(ii) Bhagat gets his share from Bharat and Bhushan in the ratio of 3 : 5,
(iii) Bhagat gets his share from Bharat alone,
(iv) Bhagat gets his share from Bhushan alone, and
(v) Bhagat gets his share from Bharat 5/40 and from Bhushan 3/40.

Explanation

(i) When Bhagat gets his share equally from old partners.
Bhagat acquires from Bharat `=(1)/(2)"of" (1)/(5)=(1)/(10)`
Form Bhushan `=(1)/(2)"of" (1)/(5)=(1)/(10)`
New Share = Old Share -Sacrifice
Hence, Bharat's New Share
`(5)/(8)-(1)/(10)=(50-8)/(80)=(42)/(80)`
Bhushan's New Share `=(5)/(8)-(1)/(10)=(30-8)/(80)=(22)/(80)`
Bhagat's Share `(1)/(5)or(16)/(80)`
Thus, New Profit-sharing Ratio `-(42)/(80):(22)/(80):(16)/(80)=21:11:8`.
(ii) When Bhagat his share from Bharat and Bhushan in the ratio of 3 : 5.
Bhagat gets his share from Bharat `=(3)/(8)"of"(1)/(5)=(3)/(40)`
From Bhushan `=(5)/(8)"of"(1)/(5)=(5)/(40)` Bharat's New Share `(5)/(8)-(3)/(40)=(25-3)/(40)=(22)/(40)`
Bhushan's New Share `=(3)/(8)-(5)/(40)=(15-5)/(40)=(10)/(40)`
Bhagat's Share `=(1)/(5)or(8)/(40)`
Thus, New Profit-sharing Ratio `=(22)/(40):(10)/(40):(8)/(40)=11:5:4`.
(iii) When Bhagat gets his share from Bharat alone.
Bharat's New Share `=(5)/(8)-(1)/(5)=(25-8)/(40)=(17)/(40)`
Bhushan's Share `=(3)/(8)or(15)/(40)` Bharat's Share `(1)/(5)or(25)/(40)`
Thus, New Profit-sharing Ratio `=(17)/(40):(15)/(40):(8)/(40)=17:15:8`.
(iv) When Bhagat gets his share from Bhushan alone.
Bharat's Share `=(5)/(8)or(25)/(40)`
Bhushan's New Share `=(3)/(8)-(1)/(5)=(15-8)/(40)=(7)/(40)`
Bhagat's Share `(1)/(5)or(8)/(40)`
Thus, New Profit-sharing Ratio `=(25)/(40):(7)/(40):(8)/(40)=25:7:8`.
(v) When Bhagat gets his share from Bharat 5/40 and from Bhushan 3/40.
Bharat's New Share `=(5)/(8)-(5)/(40)=(25-5)/(40)=(20)/(40)`
Bhushan's New Share `=(3)/(8)-(3)/(40)=(15-3)/(40)=(12)/(40)`
Bhagat's Share `(5)/(40)+(3)/(40)=(8)/(40)`
Thus, New Profit-sharing Ratio `=(20)/(40):(12)/(40):(8)/(40)=5:3:2.`