Question

geeta sold two washing machines at rs.120000 each.on one she gains 25% and on other she loses 25%.how much percent does she gain or loss in the whole transaction.

Answer 1

$\huge \sf \underline{ \red{{{answer : }}}}$

$\huge{ \blue{6.25\%}}$

$\bf{ \underline{ \underline{proof : }}}$

$\sf{s.p \: = \: 12000}$

$\sf{let \: us \: find \: c.p \: at \: 25\% \: gain}$

$\bf{c.p = \frac{s.p \times 100}{(100 + gain\%)} }$

$\bf{ ⟹\frac{12000 \times 100}{100 + 25} }$

$\bf{ \red{⟹9600}}$

$\blue{ \boxed{\boxed{ \bf{cp \ \: : 9600}}}}$

$\sf{let \: us \: find \: c.p \: 25\% \: loss}$

$\bf{c.p = \frac{s.p \times 100}{(100 - loss\%)} }$

$\bf{ ⟹\frac{12000 \times 100}{100 - 25} }$

$\bf{⟹ \frac{1200000}{75} }$

$\bf{ \red{⟹160000 }}$

$\blue{ \boxed{\boxed{ \bf{cp \ \: : 16000}}}}$

$\sf \red{\boxed {{{{cp \: of \: both \: machines \ \: : }}}}}$

$\sf{⟹16000 + 9600}$

$\sf{⟹25600}$

$\sf \red{\boxed {{{{sp \: of \: both \: machines \ \: : }}}}}$

$\sf{⟹12000 + 12000}$

$\sf{⟹24000}$

$\sf \red{loss \: \ \: : \: s.p - \: c.p}$

$\sf{⟹25600 - 24000}$

$\sf{⟹1600}$

$\boxed {\bf \red{loss\% = \frac{loss \times 100}{c.p} }}$

$\sf{⟹ \frac{1600 \times 100}{25600} }$

$\sf⟹ \frac{160000}{25600}$

$\bf \red{⟹6.25\%}$✅