Question

A,B,C are partners sharing profit in the ratio of 3:3:1. B dies. What will be the gaining ratio between A and C.​

Answer 1

ratio between a and c because B dies 3:1

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

GIVEN

• A,B,C are partners sharing profit in the ratio of 3:3:1

• B dies

TO DETERMINE

The gaining ratio between A and C

CALCULATION

$\sf{ A,B,C \: are \: partners \: sharing \: profit \: in \: the \: ratio \: \: 3:3:1\: }$

$\displaystyle \sf{ A's \: \: share \: = \frac{3}{3 + 3 + 1} = \frac{3}{7} \: }$

$\displaystyle \sf{ B's \: \: share \: = \frac{3}{3 + 3 + 1} = \frac{3}{7} \: }$

$\displaystyle \sf{ C's \: \: share \: = \frac{1}{3 + 3 + 1} = \frac{1}{7} \: }$

$\sf{Now \: B \: retires}$

$\sf{Now \: the \: new \: profit\: sharing \: ratio\: of \:A \: and \: C = 3 : 1}$

$\therefore \: \displaystyle \sf{ A's \: new \: \: share \: = \frac{3}{ 3 + 1} = \frac{3}{4} \: }$

$\therefore \: \displaystyle \sf{ C's \:new \: share \: = \frac{1}{ 3 + 1} = \frac{1}{4} \: }$

$\sf{Now \: Gaining \: Ratio \: = New \: Ratio - Old \: Ratio}$

$\therefore \: \displaystyle \sf{ A's \: gaining \: ratio \: = \frac{3}{4} - \frac{3}{7} \: } = \frac{9}{28}$

$\therefore \: \displaystyle \sf{C 's \: gaining \: ratio \: = \frac{1}{4} - \frac{1}{7} \: } = \frac{3}{28}$

$\sf{Hence \: the \: Gaining \: Ratio \: between \: A \: and \: C}$

$= \displaystyle \sf{ \frac{9}{28} : \frac{3}{28} }$

$= \displaystyle \sf{ 9 : 3 }$

$= \displaystyle \sf{ 3 : 1 }$

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