Question

5. 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

Solution :

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

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

$\underline{\bf{Explanation\::}}}}$

$\underbrace{\sf{1^{st}\:Case\::}}$

• A shopkeeper bought V.C.R (C.P) = Rs.8000
• On V.C.R loss = 4%
• Selling price ?

$\bigstar$Using formula of the selling price, while become loss :

$\longrightarrow\sf{S.P.=\bigg(\dfrac{100-loss\%}{100} \bigg)\times C.P}\\\\\\\longrightarrow\sf{S.P.=\bigg(\dfrac{100-4}{100}\bigg) \times 8000}\\\\\\\longrightarrow\sf{S.P.=\dfrac{96}{\cancel{100}} \times 80\cancel{00}}\\\\\\\longrightarrow\sf{S.P.=Rs.(96\times 80)}\\\\\\\longrightarrow\bf{S.P.=Rs.7860}$

$\underbrace{\sf{2^{nd}\:Case\::}}$

• A shopkeeper bought T.V. (C.P) = Rs.8000
• On T.V. gain = 8%
• Selling price ?

$\bigstar$Using formula of the selling price, while become profit :

$\longrightarrow\sf{S.P.=\bigg(\dfrac{100+profit\%}{100} \bigg)\times C.P}\\\\\\\longrightarrow\sf{S.P.=\bigg(\dfrac{100+8}{100}\bigg) \times 8000}\\\\\\\longrightarrow\sf{S.P.=\dfrac{108}{\cancel{100}} \times 80\cancel{00}}\\\\\\\longrightarrow\sf{S.P.=Rs.(108\times 80)}\\\\\\\longrightarrow\bf{S.P.=Rs.8640}$

Now;

Total cost price of V.C.R & T.V.= Rs.8000 + Rs.8000 = Rs.16000

Total selling price of V.C.R & T.V.= Rs.7860 + Rs.8640 = Rs.16500

$\bf{S.P.>C.P.}$

Profit = Selling price - Cost price

Profit = Rs.16500 - Rs.16000

Profit = Rs.500

So;

$\longrightarrow\sf{Profit\:\%=\bigg(\dfrac{Profit}{C.P.} \times 100\bigg)\%}\\\\\\\longrightarrow\sf{Profit\:\%=\bigg(\dfrac{500}{160\cancel{00}} \times \cancel{100}\bigg)\%}\\\\\\\longrightarrow\sf{Profit\:\%=\bigg(\cancel{\dfrac{500}{160}} \bigg)\%}\\\\\\\longrightarrow\bf{Profit\:\%=3.12\%}$

Thus;

The gain% of a shopkeeper will be 3.12% on the whole transaction .