Question

(C). P. Q and R were partners in a firm sharing profits in the ratio of 3:21
They admitted S as a new partner for 1/8th share in the profits which he acquired
1/16th from P and 1/16th from Q. Calculate new profit sharing ratio of P, Q, R and S
(C.B.S.E. 2016. Compit,​

Answer 1

Given : P , Q and R were partners in a firm sharing profits in the ratio of 3:2:1 . They admitted S as a new partner for $\sf\dfrac{1}{8} th$ share in the profits which he acquired $\sf\dfrac{1}{16} th$ from both P & Q .

Exigency to find : The new profit sharing ratio of P, Q, R and S .

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

Given that ,

⠀⠀⠀⠀⠀P , Q and R were partners in a firm sharing profits in the ratio of 3:2:1 .

⠀⠀Or ,

⠀⠀⠀⠀⠀P , Q and R were partners in a firm sharing profits in the ratio of $\bf\dfrac{3}{6}\:: \dfrac{2}{1}\:: \dfrac{1}{6}$

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:According \: To \: \: the \: Given \: Question \::}}$

⠀⠀⠀⠀⠀━━━The new Partner S's Profit share is $\bf\dfrac{1}{8} th$ [ Acquired $\bf \dfrac{1}{16} th \:$ share each from both P & Q . ]

⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀R's Profit Share = $\bf\dfrac{1}{6}$

⠀⠀⠀⠀⠀P's new Profit Share = $\bf\dfrac{3}{6} - \dfrac{1}{16} \:\:= \dfrac{21}{48}$

⠀⠀⠀⠀⠀Q's new Profit Share = $\bf\dfrac{2}{6} - \dfrac{1}{16} \:\:= \dfrac{13}{48}$

⠀⠀⠀⠀⠀S's Profit Share = $\bf\dfrac{1}{8}$

Therefore,

• The New Profit Share Ratio of P , Q , R & S is $\bf\dfrac{21}{48}\:: \dfrac{13}{48}\:: \dfrac{1}{6}\:: \dfrac{1}{8}$

⠀⠀⠀⠀⠀Or ,

• The New Profit Share Ratio of P , Q , R & S is 21 : 13 : 8 : 6

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:The\:New\:Profit \;Sharing \:Ratio\:is\:\:\bf{21:13:8:6}}}}$

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