Question

X.Y.Z are partners in a firm sharing profits and losses of the firm as 1/2, 1/5, 1/10 & and 1/5 respectively.
R has expired. Surviving partners p.Q and s taje up R's ratio in the proportion of 3:2:1

Find out new ratio of P.Q.& S​

Answer 1

$\huge\boxed{ \underline{ \underline{ \bf{Answer}}}}$

New Gain Ratio Of P,Q & R is ;

P = $\frac{33}{60}$

Q = $\frac{14}{60}$

R = $\frac{13}{60}$

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${ \underline{ \underline { \bf{Explaination\::-}}}}$

Old ratio of P , Q , & R is $\frac{1}{2} ; \frac{1}{5} and \frac{1}{10}$ ...... ( Given )

Gain Ratio = R's ratio × Take up Proportion.

P"s Gain Ratio = $\frac{1}{10}$ × $\frac{3}{6}$ = $\frac{3}{60}$

Q's Gain Ratio = $\frac{1}{10}$ × $\frac{2}{6}$ = $\frac{2}{60}$

S's Gain Ratio =  $\frac{1}{10}$ × $\frac{1}{6}$ = $\frac{1}{60}$

NEW RATIO = OLD RATIO + GAIN RATIO

∴ P's New Ratio = $\frac{1}{2}$ + $\frac{3}{60}$

                          = $\frac{30+3}{60}$

                          = $\frac{33}{60}$

∴ Q's New Ratio = $\frac{1}{5}$ + $\frac{2}{60}$

                           = $\frac{12+2}{60}$

                           = $\frac{14}{60}$

∴ S's New Ratio = $\frac{1}{5}$ + $\frac{1}{60}$

                           =  $\frac{12+1}{60}$

                           = $\frac{13}{60}$

∴ hence proved that ,

New Ratio of P, Q and S is $\frac{33}{60}$ ; $\frac{14}{60}$ And  $\frac{13}{60}$

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