Question

X and y are partner sharing profit and losses in the ratio of 5:3 they admit z for 1/4th share in the profit and agree to share b/w them in the ratio of 2:1 in future calculate the sacrifice ratio​

Answer 1

$\huge\mathbb\purple{AnSwEr}$

$\sf \: old \: ratio \: of \: partners \: = 5:3 \\ \sf \: share \: of \: z = \frac{1}{4} \\ \sf \: new \: ratio \: of \: partners \: = 2:1:1$

• To find sacrificing ratio:-

$\sf\purple \: old \: ratio - new \: ratio$

$\sf \: sacrificing \: ratio \: of \: x = > \\ \sf \: old \: ratio = \frac{5}{8} \\ \ \sf new \: ratio = \frac{2}{4} \\ \sf \implies\: \frac{5}{8} - \frac{2}{4} = \frac{5}{8} - \frac{2 \times 2}{4 \times 2} = \frac{4}{8} \\ \sf\implies \: \frac{5}{8} - \frac{4}{8} = \frac{1}{8}$

$\sf \: sacrificing \: ratio \: of \: y = > \\ \sf \: old \: ratio = \frac{3}{8} \\ \sf \: new \: ratio = \frac{1}{4} \\ \sf \: \implies \frac{3}{8} - \frac{1}{4} = \frac{3}{8} - \frac{1 \times 2}{4 \times 2} = \frac{2}{8} \\ \sf\implies \: \frac{3}{8} - \frac{2}{8} = \frac{1}{8}$

$\rm\red{ \: so \: \: sacrificing \: ratio \: of \: x \: and \: y = 1: 1}$