Question

5. A VCR and TV were bought for 2 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 in
percent on the whole transaction. ​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

A VCR and TV were bought for 2 8,000 each.

The shopkeeper made a loss of 4% on the VCR and a profit of 8% on the TV.

Case :- 1

Cost Price of VCR = 28000

Loss % = 4 %

We know,

$\rm \: \boxed{ \rm{ \:Selling \: Price \: = \: \frac{(100 - Loss\%) \times Cost \: Price}{100} \: }}$

So, on substituting the values, we get

$\rm \: Selling \: Price = \dfrac{(100 - 4) \times 28000}{100}$

$\rm \: Selling \: Price = 96 \times 280$

$\rm\implies \:Selling \: Price \: = \: 26880$

Case :- 2

Cost Price of TV = 28000

Profit % = 8 %

We know that

$\rm \: \boxed{ \rm{ \:Selling \: Price \: = \: \frac{(100 + Profit\%) \times Cost \: Price}{100} \: }}$

So, on substituting the values, we get

$\rm \: Selling \: Price = \dfrac{(100 + 8) \times 28000}{100}$

$\rm \: Selling \: Price \: = \: 108 \times 280$

$\rm\implies \:Selling \: Price \: = \: 30240$

So,

Total Cost Price = 28000 + 28000 = 56000

Total Selling Price = 26880 + 30240 = 57120

Since, Selling Price > Cost Price

It implies, there is gain in this transaction.

$\rm \: Profit\% = \dfrac{Selling \: Price - Cost \: Price}{Cost \: Price} \times 100\%$

$\rm \: Profit\% = \dfrac{57120 - 56000}{56000} \times 100\%$

$\rm \: Profit\% = \dfrac{1120}{560} \%$

$\rm\implies \:\boxed{ \rm{ \:\rm \: Profit\% = 2 \% \: \: }}$

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{Gain = \sf S.P. \: – \: C.P.} \\ \\ \bigstar \:\bf{Loss = \sf C.P. \: – \: S.P.} \\ \\ \bigstar \: \bf{Gain \: \% = \sf \Bigg( \dfrac{Gain}{C.P.} \times 100 \Bigg)\%} \\ \\ \bigstar \: \bf{Loss \: \% = \sf \Bigg( \dfrac{Loss}{C.P.} \times 100 \Bigg )\%} \\ \\ \\ \bigstar \: \bf{S.P. = \sf\dfrac{(100+Gain\%) or(100-Loss\%)}{100} \times C.P.} \\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$