Question

Question of the day....

A man sold two washing machine for Rs. 7500 each. On one he gains 25 % and on other he loses 25 %. Find the gain or lose percentage.​

Answer 1

$\bf \: \underline{Given} :$ ↴

$\sf \: A \: man \: sold \: two \: washing \: machine \: for \: Rs. \: 7500 \: each.$

$\sf \: On \: one \: he \: gains \: 25 \: \% \: and \: on \: other \: he \: loses \: 25 \%.$

$\bf \: \underline{To \: find} :$ ↴

$\sf \: We \: have \: to \: find \: his \: gain \: or \: lose \: percentage.$

$\bf \: \underline{\underline{Solution} }$

$\sf \: \underline{ First \: of \: all \: we \: will \: find \: the \: C.P \: of \: first \: washing \: machine}.$

$\sf \: Here,$

$\sf \: S.P \: of \: first \: washing \: machine = Rs. 7500$

$\sf \: Gain \: \% = 25 \: \%$

$\sf \:\implies \: \boxed{ \sf \pink{C.P = \dfrac{100}{(100 +Gain \%) } \: \times \: S.P }}$

$\sf \: \implies \:C.P = \dfrac{100}{(100 +25) } \: \times \: 7500$

$\sf \:\implies \: C.P = \dfrac{100}{125} \: \times \: 7500$

$\sf \: \red{\implies \: C.P \: of \: first \: washing \: machine= Rs. \: 6000}$

$\sf \: \underline{Now, \: we \: will \: find \: the \: C.P \: of \: second \: washing \: machine}.$

$\sf \: Here,$

$\sf \: S.P \: of \: second \: washing \: machine = Rs. 7500$

$\sf \: Loss \: \% = 25 \: \%$

$\sf \: \implies \:\boxed{\sf \pink{C.P = \dfrac{100}{(100 - Loss \%) } \: \times \: S.P}}$

$\sf \: \implies \:C.P = \dfrac{100}{(100 - 25\%) } \: \times \: 7500$

$\sf \: \implies \:C.P = \dfrac{100}{75 } \: \times \: 7500$

$\sf \red{\implies \: C.P \: of \: second \: washing \: machine= Rs. \: 10,000}$

$\bf \: So,$

$\sf \: Total \: C.P \: of \: both \: washing \: machine =Rs. \: ( 6000 + 10,000) = Rs. \: 16,000$

$\sf \: Total \: S.P \: of \: both \: washing \: machine =Rs. \: ( 7500 + 7500)= Rs. \: 15,000$

$\sf \: \: Here \: S.P > C.P \: \: \: \: \underline{So, \: Loss \: is \: there}$

$\sf \:\implies \: Loss = C.P - S.P$

$\sf \:\implies \: Loss =Rs. \: ( 16000 - 15000 )$

$\sf \:\implies \: Loss = Rs. \: 1000$

$\sf \: \implies \:\boxed{ \sf \pink{\: Loss \: \% = \dfrac{Loss}{C. P } \: \times \: 100}}$

$\sf \:\implies \: Loss \: \% = \dfrac{1000}{16000} \: \times \: 100$

$\implies \underline{\boxed{ \green{ \sf \: Loss \: \% = 6.25 \: \% }}}$

Answer 2

Answer:

• Man get loss of 6.25% on whole transaction

Explanation:

Given:

• Man sold two washing machine at ₹7500 each
• On one machine, he gain 25%
• On another machine, he loss 25%

To find:

• Gain or loss percentage of man

Solution:

Here, it is given that man sold two machines at ₹7500 each in which he gain 25% on one machine but he loses 25% on another machine.

Now, to find gain/loss percentage, we need to find cost price (CP) of machine first.

We know that :

• $\large{\boxed{\sf{\pink{CP\:=\: \dfrac{100}{100+gain\%(-loss\%)}×SP}}}}$

Finding CP of first machine ( of 25% gain):-

Given that :

• SP = ₹7500
• gain = 25%

Let put the given value in formula:-

$\large{\sf{CP\:=\:\dfrac{100}{100+gain\%}×SP}}$

$\implies\large{\sf{CP\:=\:\dfrac{100}{100+25}×7500}}$

$\implies\large{\sf{CP\:=\:\dfrac{100}{125}×7500}}$

$\implies\large{\sf{CP\:=\:\dfrac{100}{\cancel{125}}×{\cancel{7500}}}}$

$\implies\large{\sf{CP\:=\:100×60}}$

$\implies\large{\sf{CP\:=\:6000}}$

Therefore,

• Cost price of this washing machine is ₹6000.

_______________

Finding CP of second machine (of 25% loss):-

Given that:

• SP = ₹7500
• loss = 25%

Let put the given value in formula :-

$\large{\sf{CP\:=\:\dfrac{100}{100-loss\%}×SP}}$

$\implies\large{\sf{CP\:=\:\dfrac{100}{100-25}×7500}}$

$\implies\large{\sf{CP\:=\:\dfrac{100}{75}×7500}}$

$\implies\large{\sf{CP\:=\:\dfrac{100}{\cancel{75}}×{\cancel{7500}}}}$

$\implies\large{\sf{CP\:=\: 100×100}}$

$\implies\large{\sf{CP\:=\:10000}}$

Therefore,

• Cost price of second machine is ₹10000

_______________

Now, we find that CP of both machines are ₹6000 and ₹10000 respectively and SP is ₹7500 each as given.

Therefore,

• Total CP of both machines is ₹6000+₹10000 = ₹16000
• Total SP of both machines is ₹7500+₹7500 = ₹15000

What we found from here? we can see that here SP < CP. If SP<CP then there will loss.

• Loss = CP - SP = 16000-15000 = ₹1000

We have :

• CP = ₹16000
• SP = ₹15000
• Loss = ₹1000

We know that :

• $\large{\boxed{\sf{\pink{Loss\%\:=\:\dfrac{loss×100}{CP}}}}}$

Let put the given value in formula :

$\large{\sf{Loss\%\:=\: \dfrac{loss×100}{CP}}}$

$\implies\large{\sf{Loss\%\:=\: \dfrac{1000×100}{16000}}}$

$\implies\large{\sf{Loss\%\:=\:\dfrac{100000}{16000}}}$

$\implies\large{\sf{Loss\%\:=\: {\cancel{\dfrac{100000}{16000}}}}}$

$\implies\large{\sf{Loss\%\:=\: 6.25\%}}$

Therefore,

• $\large{\boxed{\sf{\red{Man\:get\:loss\:on\:whole\: transaction\:of\:6.25\%}}}}$