Question

Geeta sold two washing machines at 1,20,000
each. On one she gains 25% and on the other she
loses 25%. How much per cent does she gain or
lose in the whole transaction?
(2)​

Answer 1

Question :-

• Geeta sold two washing machines at Rs 120000 each. On one she gains 25% and on the other she loses 25%. How much per cent does she gain or lose in the whole transaction ?

Given:

• SP of each washing machine = Rs 120000
• In first washing machine :- gain% = 25%
• In second washing machine:-loss% = 25%

To Find :

• Gain% or loss%.

Solution:-

$\sf{Total \:SP= Rs\:(120000+120000) = Rs\:240000}$

★In First washing machine :

• SP =Rs 120000
• Gain%=25%

$:\implies {\sf{CP=Rs\:\bigg[\dfrac{100}{(100+25)} \times 120000\bigg]}} \\ \\ :\implies {\sf{CP=Rs\:\bigg(\dfrac{100}{\cancel{125}} \times \cancel{120000}\bigg)}}\\ \\ :\implies {\sf{CP=Rs\:(100\times 960)}}\\ \\ :\implies{\boxed{\tt{CP=Rs\:96000}}}$

★In Second washing machine :

• SP=120000
• Loss% =25%

$:\implies {\sf{CP=Rs\:\bigg[\dfrac{100}{(100-25)} \times 120000\bigg]}}\\ \\ :\implies {\sf{CP=Rs\: \bigg(\dfrac{100}{\cancel{75}}\times\cancel{120000} \bigg)}}\\ \\ :\implies {\sf{CP=Rs\:(100\times 1600)}}\\ \\ : \implies{\boxed{\tt{CP=Rs\:160000}}}$

$\sf {Total \: CP= Rs\:(96000+160000) = Rs\:256000}$

$\tt{\because {CP>SP,\:there\:is\: a \:loss.}}$

◆Finding loss :

$:\implies{\sf{Loss = CP-SP}}\\ \\:\implies {\sf{Loss=Rs\:(256000-240000)}}\\ \\ : \implies { \boxed{\tt{Loss=Rs\:16000}}}$

◆Finding loss% :

$:\implies{\sf{Loss\% = \bigg( \dfrac{Loss}{CP } \times 100} \bigg)\%} \\ \\ :\implies{\sf{Loss\% = \bigg(\dfrac{16000}{2560 \cancel{00}}} \times 1{ \cancel{00} \bigg)\%}}\\ \\ :\implies{\sf{Loss\% = \bigg( \dfrac{16000}{2560 } \bigg)\%}} \\ \\:\implies{ \boxed{\tt{Loss\% = 6.25\%}}}$

$\therefore{\underline{\sf{She\:loses\:\bf{6.25\%}\: \sf{in \:the\:whole \:transaction.}}}}$

Answer 2

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

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

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

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

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

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

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

$\bf{ \red{⟹9600}}$

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

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

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

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

$\bf{⟹ \frac{1200000}{75} }$

$\bf{ \red{⟹160000 }}$

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

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

$\sf{⟹16000 + 9600}$

$\sf{⟹25600}$

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

$\sf{⟹12000 + 12000}$

$\sf{⟹24000}$

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

$\sf{⟹25600 - 24000}$

$\sf{⟹1600}$

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

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

$\sf⟹ \frac{160000}{25600}$

$\bf \red{⟹6.25\%}$