Question

find the sacrificing ratio and new ratio in the following
1. A and B are the partners sharing profit and losses in the ratio of 3:2. C is admitted for 1/4th share. A and B decided to share equality in future. ​

Answer 1

Question:-

To find sacrificing ratio and new ratio

Solution:-

$\sf \: old \: ratio \: of \: partners \: = 3:2$

$\sf \: share \: of \: c = \frac{1}{4}$

$\sf \: remaining \: portion = 1 - \frac{1}{4} = \frac{3}{4}$

To find new ratio:-

$\rm\blue{ \: old \: ratio \: \times remaining \: portion \: }$

$\sf \: new \: share \: of \: a = \frac{3}{5} \times \frac{3}{4} = \frac{9}{20}$

$\sf \: new \: share \: of \: b = \frac{2}{5} \times \frac{3}{4} = \frac{6}{20}$

$\sf \: share \: of \: c = \frac{1}{4} = \frac{5}{20}$

$\rm\implies\red{ \: new \: ratio = 9: 6 : 5}$

To find sacrificing ratio:-

$\rm\blue{ \: old \: ratio - new\: ratio}$

$\sf \: sacrificing \: ratio \: of \: a = \frac{3}{5} - \frac{9}{20} = \frac{3 \times 4}{5 \times 4} - \frac{9}{20} = \frac{12 - 9}{20} = \frac{3}{20}$

$\sf \: Sacrificing \: ratio \: of \: b = \frac{2}{5} - \frac{6}{20} = \frac{2 \times 4}{5 \times 4} - \frac{6}{20} = \frac{8 - 6}{20} = \frac{2}{20}$

$\rm\implies\green{ \: sacrificing \: ratio = 3: 2}$

so, the old ratio and sacrificing ratio is same.