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?​

Answer 1

$\bf{\red{\Large{\boxed{\tt{ANSWER\::}}}}}}$

6.25%

$\bf{\Large{\green{\underline{\underline{\sf{Given\::}}}}}}$

Geeta sold two washing machines at 120000 each. On one she gains 25% and on the other she loses 25%.

$\bf{\Large{\red{\underline{\underline{\bf{To\:find\::}}}}}}$

The percentage does she gains or loss in the whole transaction.

$\bf{\Large{\purple{\underline{\underline{\sf{Explanation\::}}}}}}$

Total Selling price (S.P.) of machine = (120000+120000) = Rs.240000

$\bf{\orange{\large{\underline{\underline{\tt{\blacksquare{She\:gains\:25\%\::}}}}}}}$

Formula use :

$\bf{\large{\boxed{\sf{Cost\:price\:(C.P.)=\bigg(\frac{100}{100+gain\%}\bigg) \times S.P.}}}}}}$

A/q

$\leadsto\tt{C.P.=\bigg(\dfrac{100}{100+25} \bigg)*120000}\\\\\\\\\leadsto\tt{C.P.=\dfrac{100}{\cancel{125}} *\cancel{120000}}\\\\\\\\\leadsto\tt{C.P.=Rs.(100\times 960)}\\\\\\\\\leadsto\tt{\green{C.P.=Rs.96000}}$

__________________________________________

$\bf{\orange{\large{\underline{\underline{\tt{\blacksquare{She\:losses\:25\%\::}}}}}}}$

Formula use :

$\bf{\large{\boxed{\sf{Cost\:price\:(C.P.)=\bigg(\frac{100}{100-loss\%}\bigg) \times S.P.}}}}}}$

A/q

$\leadsto\tt{C.P.=\bigg(\dfrac{100}{100-25} \bigg)*120000}\\\\\\\\\leadsto\tt{C.P.=\dfrac{100}{\cancel{75}} *\cancel{120000}}\\\\\\\\\leadsto\tt{C.P.=Rs.(100\times 1600)}\\\\\\\\\leadsto\tt{\green{C.P.=Rs.160000}}$

Now,

Total Cost price = Rs.(96000 + 160000) = Rs.256000

We can consider here that Geeta found loss :

$\mapsto\sf{Loss = Cost\:price -Selling\:price}\\\\\\\mapsto\sf{Loss=Rs.(256000-240000)}\\\\\\\mapsto\sf{\red{Loss=Rs.16000}}$

$\bf{\orange{\large{\underline{\underline{\tt{\blacksquare{She\:loss\:percentage\:in\:whole\:transaction\::}}}}}}}$

$\hookrightarrow\tt{Loss\%=\dfrac{loss*100}{C.P.} }\\\\\\\\\hookrightarrow\tt{Loss\%=\dfrac{16000*\cancel{100}}{2560\cancel{00}} }\\\\\\\\\hookrightarrow\tt{Loss\%=\cancel{\dfrac{16000}{2560}} }\\\\\\\\\hookrightarrow\tt{\pink{Loss\%=6.25\%}}$

∴ The whole transaction is 6.25 %.

Answer 2

||✪✪ 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?

|| ✰✰ ANSWER ✰✰ ||

Case 1 :-

→ SP = 1,20.000

→ Gain = 25%

→ CP = (SP * 100) / (100 + Gain%)

→ CP = (120000 * 100) / (125)

→ CP = 96000

______________

Case 2 :-

→ SP = 1,20.000

→ Loss = 25%

→ CP = (SP * 100) / (100 - Loss%)

→ CP = (120000 * 100) / (75)

→ CP = 160000

___________

Now,

→ All over SP = 2*120000 = 240000

→ All over CP = 96000 + 160000 = 256000

So,

→ Total Loss = CP - SP = 256000 - 240000 = 16000

____________

So ,

→ Overall Loss % = ( total Loss * 100) / ( Total CP)

→ Overall Loss % = (16000 * 100) / (256000)

→ Overall Loss % = 6.25% .

Hence, Geeta has a loss of 6.25% in the whole transaction .

__________________________

✭✫ Shortcut Trick ✫✭ :-

When Two Items Are Sold At Same SP, and In one We have Profit of X % and on other Item we have Loss of X % Than , Overall We Always Have A Loss of :-

☛ Loss % = (X)² / 100

Our Question it was given That, 2 washing machine were Sold at Same SP as 120000 . One One Geeta has a loss of 25% and on other machine she has a gain of 25% .

So, we can say That :-

☞ She Has overall Loss of = (25)² / 100 = (625)/100 = 6.25% .

⟦ with This Trick we can Solve This Question in 5 seconds . ⟧

Hence, Geeta has a loss of 6.25% in the whole transaction.

_____________________________