Question

​​​​​​​​♤ Moderators ⭐ Branily star ❤️ other best user Question <<< please answer this question urgently fast answer no spam no spam no spam​​​​​​​​​​​​​​

Answer 1

$\red{\textbf{Answer :-}}$

$D \: admitted \: for \: \LARGE \frac{4}{7}$$share \: of \: profit \: in \: new \: firm$

$\red{\textbf{D's \: share = }}$

$\blue{\textit{A`s sacrifice + B`s sacrifice + C`s sacrifice}}$

=$\LARGE\frac{4}{7} = \frac{2}{7} +\frac{1}{7} +\frac{1}{7}$

$\red{\textbf{New ratio =}}$

$\blue{\textit{Old Ratio}}$- $\blue{\textit{Old sacrificing ratio}}$

$A = \LARGE \frac{3}{8} - \frac{2}{7 }$

$= \LARGE\frac{21 - 16}{56}$$= \LARGE\frac{5}{56}$

$B = \LARGE \frac{3}{8} - \frac{1}{7 }$

$= \LARGE\frac{21 - 8}{56}$$= \LARGE\frac{13}{56}$

$C= \LARGE\frac{2}{8} - \frac{1}{7}$

$= \LARGE \frac{14 - 8}{56}$$= \LARGE\frac{6}{56}$

$\LARGE\frac{5}{56} : \frac{13}{56} : \frac{6}{56} : \frac{4}{7}$

$= \LARGE \frac{5:13:6:32}{56}$

$= 5:13:6:32$

$\red{\textbf{So, New profit sharing ratio =}}$

$= 5:13:6:32$

Answer 2

Given :-

• A, B, C were partners in a firm sharing profits in 3 : 3 : 2 ratio.
• They admitted D as a new partner for 4/7 profit.
• D acquires his share 2/7 from A.
• 1/7 from B and 1/7 from C.

To Find :-

• What is the new profit sharing ratio.

Solution :-

❒ In case of Old Ratio :

$\leadsto \sf\bold{Old\: ratio =\: A : B : C}$

$\leadsto \sf\bold{Old\: ratio =\: 3 : 3 : 2}$

Hence, the old ratio of A, B and C were :

➲ Old Ratio Of A :

$\implies \sf Old\: Ratio\: Of\: A =\: \dfrac{3}{3 + 3 + 2}$

$\implies \sf\bold{\purple{ Old\: Ratio\: Of\: A =\:\dfrac{3}{8}}}$

➲ Old Ratio Of B :

$\implies \sf Old\: Ratio\: Of\: B =\: \dfrac{3}{3 + 3 + 2}$

$\implies \sf \bold{\purple{Old\: Ratio\: Of\: B =\: \dfrac{3}{8}}}$

➲ Old Ratio Of C :

$\implies \sf Old\: Ratio\: Of\: C =\: \dfrac{2}{3 + 3 + 2}$

$\implies \sf\bold{\purple{Old\: Ratio\: Of\: C =\: \dfrac{2}{8}}}$

Now,

$\bigstar$ They admitted D as a new partner for 4/7 profit.

Hence, D's share will be :

$\small\leadsto \sf\bold{\pink{D's\: Share =\: A's\: Sacrifice + B's\: Sacrifice + C's\: Sacrifice}}$

$\implies \bf{ \dfrac{4}{7} =\: \dfrac{2}{7} + \dfrac{1}{7} + \dfrac{1}{7}}$

Now, we have to find the new ratio of A, B and C :

As we know that :

$\clubsuit$ New Ratio Formula :

$\footnotesize\mapsto \sf\boxed{\bold{\pink{New\: Ratio =\: Old\: Ratio - Sacrificing\: Ratio}}}$

Hence, new ratio of A, B and C were :

▣ New Ratio Of A :

$\implies \sf New\: Ratio\:Of\: A =\: \dfrac{3}{8} - \dfrac{2}{7}$

$\implies \sf New\: Ratio\: Of\: A =\: \dfrac{21 - 16}{56}$

$\implies \sf \bold{\green{New\: Ratio\: Of\: A =\: \dfrac{5}{56}}}$

▣ New Ratio Of B :

$\implies \sf New\: Ratio\: Of\: B =\: \dfrac{3}{8} - \dfrac{1}{7}$

$\implies \sf New\: Ratio\: Of\: B =\: \dfrac{21 - 8}{56}$

$\implies \sf\bold{\green{New\: Ratio\: Of\: B =\: \dfrac{13}{56}}}$

▣ New Ratio Of C :

$\implies \sf New\: Ratio\: Of\: C =\: \dfrac{2}{8} - \dfrac{1}{7}$

$\implies \sf New\: Ratio\: Of\: C =\: \dfrac{14 - 8}{56}$

$\implies \sf\bold{\green{New\: Ratio\: Of\: C =\: \dfrac{6}{56}}}$

Now, we have to find the new profit sharing ratio of A, B, C and D :

$\leadsto \bf{New\: Ratio =\: A : B : C : D}$

$\leadsto \bf{New\: Ratio =\: \dfrac{5}{56} : \dfrac{13}{56} : \dfrac{6}{56} : \dfrac{4}{7}}$

$\longrightarrow \sf New\: Ratio =\: \dfrac{5 : 13 : 6 : 32}{56}$

$\longrightarrow \sf\bold{\red{New\: Ratio =\: 5 : 13 : 6 : 32}}$

${\small{\bold{\underline{\therefore\: The\: new\: profit\: sharing\: ratio\: is\: 5 : 13 : 6 : 32\: .}}}}$