Question

A VCR and TV were bought for 8,000 each. The shopkeeper made a
loss of 4% on the VCR and a profit of 8% on the TV. Find the gain or loss
percent on the whole transaction.​

Answer 1

$\bf{\huge{\boxed{\underline{\sf{ANSWER\::}}}}}}$

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

A VCR and T.V. were bought for Rs.8000 each. The shopkeeper made a loss of 4% on the VCR and a profit of 8% on the T.V.

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

The gain or loss percent on the whole transaction.

$\bf{\Large{\underline{\tt{\blue{Explanation\::}}}}}$

A VCR and T.V. bought for Rs.8000 each.

$\leadsto\sf{Total\:cost\:price\:(C.P.)\:=\:V.C.R. \:+\:T.V.}\\\\\leadsto\sf{Total\:cost\:price\:(C.P.)\:=\:Rs.(8000+8000)}\\\\\leadsto\sf{\red{Total\:cost\:price\:(C.P.)\:=\:Rs.16000}}$

Now,

Selling Price of VCR and T.V. ;

$\bf{\large{\boxed{\sf{Selling\:price\:(S.P.)\:of\:V.C.R.}}}}}$

• Loss = 4%
• C.P. = Rs.8000

$\implies\sf{Selling\:Price\:(S.P.)=\bigg[\dfrac{(100-loss\%)}{100} *C.P.\bigg]}\\\\\\\\\implies\sf{Selling\:price\:(S.P.)=\bigg[\dfrac{100-4}{100} *8000\bigg]}\\\\\\\\\implies\sf{Selling\:price\:(S.P.)=\bigg[\dfrac{96}{\cancel{100}} *80\cancel{00}\bigg]}\\\\\\\\\implies\sf{Selling\:price\:(S.P.)=Rs.(96*80)}\\\\\\\\\implies\sf{\red{Selling\:price\:(S.P.)=Rs.7680}}$

$\bf{\large{\boxed{\sf{Selling\:price\:(S.P.)\:of\:T.V.}}}}}$

• Profit = 8%
• C.P. = Rs.8000

$\implies\sf{Selling\:Price\:(S.P.)=\bigg[\dfrac{(100+profit\%)}{100} *C.P.\bigg]}\\\\\\\\\implies\sf{Selling\:price\:(S.P.)=\bigg[\dfrac{100+8}{100} *8000\bigg]}\\\\\\\\\implies\sf{Selling\:price\:(S.P.)=\bigg[\dfrac{108}{\cancel{100}} *80\cancel{00}\bigg]}\\\\\\\\\implies\sf{Selling\:price\:(S.P.)=Rs.(108*80)}\\\\\\\\\implies\sf{\red{Selling\:price\:(S.P.)=Rs.8640}}$

So,

$\leadsto\sf{Total\:selling\:price\:(S.P.)\:=\:V.C.R. \:+\:T.V.}\\\\\leadsto\sf{Total\:selling\:price\:(S.P.)\:=\:Rs.(7680+8640)}\\\\\leadsto\sf{\red{Total\:selling\:price\:(S.P.)\:=\:Rs.16320}}$

Therefore,

Shopkeeper made a profit :

We know that profit, we get;

$\leadsto\sf{Profit\:=\:Selling\:price\:-\:Cost\:price}\\\\\leadsto\sf{Profit\:=\:Rs.16320\:-\:Rs.16000}\\\\\leadsto\sf{\red{Profit\:=\:Rs.320}}$

Now,

$\mapsto\sf{Gain\:percentage\:=\:\dfrac{Gain}{C.P.} *100}\\\\\\\mapsto\sf{Gain\:percentage\:=\:\dfrac{320}{160\cancel{00}} *\cancel{100}}\\\\\\\mapsto\sf{Gain\:percentage\:=\:\cancel{\dfrac{320}{160} }}\\\\\\\mapsto\sf{\red{Gain\:percentage\:=\:2\%}}$

Thus,

The 2% on the whole transaction.

Answer 2

Step-by-step explanation:

Given,

A VCR and TV were bought for 8,000 each. The shopkeeper made a loss of 4% on the VCR and a profit of 8% on the TV.

To find: The gain or loss percent on the whole transaction.

Solution:- Total Cost Price

CP of the VCR + CP of TV = Total Cost Price = ₹16000

VCR:-

CP = ₹8000

Loss = 4%

Loss = Loss%/100×CP

Loss = $4\div100×8000$

Loss = ₹320

SP = CP-Loss = 8000-320 = ₹7680

TV:-

CP = ₹8000

Profit = 8%

Profit = Profit%/100×CP

Profit = $8\div100×8000$

Profit = ₹640

SP = CP+Profit = 8000+640 = ₹8640

Total SP:-

SP of VCR + SP of TV = Total SP

₹7680 + ₹8640 = Total SP

Total SP = ₹16320

-------------------—-------—

====>₹ 16320>₹ 16000

====> So, SP> CP

Hence, it's a profit.

Profit = SP-CP = 16320-16000 = ₹ 320

Profit% = Profit%/CP×100

Profit% = $320\div16000×100$

Profit% = 2%

Hence, Proved.