Question

X,Y,Z,W are 4:3:2:1 .Z acquire 1/5 from X. Y acquire 1/5 from X and W equally . Find new ratio and sacrifice ratio​

Answer 1

Answer:

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Explanation:

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Answer 2

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

Ratio of X, Y, Z, W are

$= 4 : 3 : 2: 1\:$

So

$\displaystyle \: \sf{The \: share \: of \: X = \frac{4}{10} }$

$\displaystyle \: \sf{The \: share \: of \: Y = \frac{3}{10} }$

$\displaystyle \: \sf{The \: share \: of \: Z = \frac{2}{10} }$

$\displaystyle \: \sf{The \: share \: of \: W = \frac{1}{10} }$

$\displaystyle \: \sf{Z \: acquires \: \frac{1}{5} \: from\: X }$

So

$\displaystyle \: \sf{Z \: acquires \: \: from\: X = \bigg( \: \frac{4}{10} \times \frac{1}{5} \bigg) = \frac{4}{50} }$

In case of Gaining

$\sf{ \: New \: Ratio = Old \: Ratio + Gaining \: Ratio \: }$

So

$\displaystyle \: \sf{ New \: share \: of \: \: Z\: = \frac{2}{10} + \frac{4}{50} = \frac{14}{50} }$

$\displaystyle \: \sf{Y \: acquires \: \frac{1}{5} \: from\: X \: and \:W \: equally }$

SO

$\displaystyle \: \sf{Y \: acquires \: \: from\: X = \bigg( \: \frac{4}{10} \times \frac{1}{5} \bigg) = \frac{4}{50} }$

$\displaystyle \: \sf{Y \: acquires \: \: from\: W = \bigg( \: \frac{1}{10} \times \frac{1}{5} \bigg) = \frac{1}{50} }$

$\sf{ \: New \: Ratio = Old \: Ratio + Gaining \: Ratio \: }$

$\displaystyle \: \sf{ New \: share \: of \: \: Y\: = \frac{3}{10} + \frac{4}{50} + \frac{1}{50} = \frac{14}{50} }$

In case of Sacrificing

$\sf{ \: New \: Ratio = Old \: Ratio - Sacrificing \: Ratio \: }$

$\displaystyle \: \sf{ New \: share \: of \: \: X\: = \frac{4}{10} - \frac{4}{50} - \frac{4}{50} = \frac{12}{50} }$

$\displaystyle \: \sf{ New \: share \: of \: \: W\: = \frac{1}{10} - \frac{1}{50} = \frac{4}{50} }$

RESULT

Hence the new ratio of X, Y, Z, W are

$\displaystyle \: = \frac{12}{50} : \frac{20}{50} : \frac{14}{50}: \frac{4}{50}\:$

$= 6: 10 : 7: 2\:$

Here X & W sacrifices

So the Sacrificing ratio of X and W are

$\displaystyle \: = \frac{8}{50} : \frac{1}{50}$

$= 8 : 1$