On 1st April 2010m Sahil and Charu entered into partnership for sharing profit in the ratio of 4:3. They admitted Tanu as a new partner on 1st April, 2012 of 1/5th share which she acquired equally from Sahil and Charum Charu and Tanu earned profits at a higher rate than the normal rate of return for the year ended 31st March, 2013. Therefore, they decided to expand their business. To meet the requirments of additonal capital, they admitted Puneet as a new partner on 1st April, 2013 for 1/7th share in profit which he acquried from Sahil and Charu in 7 : 3 ratio.
Calculate:
(i) New profit-sharing ration of Sahil, Charu and Tanu for the year 2012 13
(ii) New profit-sharing ratio of Sahil, Chaur, Tanu and Puneet on Puneet's admission.

Explanation

(i) Calculation of New Profit-sharing Ratio of Sahil, Charu and Tanu for th year 2012-13:
Sahil's Old Share `=(4)/(7)`
Sahil surrenders in favour of Tanu `=(1)/(5)xx(1)/(2)=(1)/(10)`
Sahil's New Share `=(4)/(7)-(1)/(10)=(33)/(70)`
Chaur's Old Share `=(3)/(7)`
Charu surrenders in favour of Tanu `=(1)/(5)xx(1)/(2)=(1)/(10)`
Charu's New Share `=(3)/(7)-(1)/(10)=(23)/(70)`
Tanu's share `=(1)/(5) or(14)/(70)`
Thus, New Profit-sharing Ratio among Sahil, Charu and Tanu `=(33)/(70):(23)/(70):(14)/(70)=33:23:14`.
(ii) New Profit-sharing Ratio of Sahil, Charu, Tanu and Puneet on Puneet's Admission:
Sahil's Old Share `=(33)/(70)`
Sahil surrenders in favour of Puneet `=(1)/(7)xx(7)/(10)=(7)/(70)`
Sahil's New Share `=(33)/(70)-(7)/(70)=(26)/(70)`
Charu's Old Share `=(23)/(70)`
Charu surrenders in favour of Puneet `(1)/(7)xx(3)/(10)=(3)/(70)`
Charu's New Share `=(23)/(70)-(3)/(70)=(20)/(70)`
Tanu's share remains the same, i.e., `(1)/(5)or(10)/(70)`
Thus, New Profit-sharing Ratio among Partners `=(26)/(70):(20)/(70):(14)/(70):(10)/(70)`
Sahil : Charu : Tanu : Puneet = 13 : 10 : 7 : 5.