Question

A man sells a radio-set for \[{\mathbf{Rs}}.{\mathbf{605}}\] and gains\[{\mathbf{10}}\% \]. At what price should he sell another radio of the same kind, in order to gain\[{\mathbf{16}}\% \]?

Answer 1

Hint: This question is a very fundamental question which mainly requires the basic concept or knowledge of Profit and Loss. It means whenever there is selling or buying of things we come to know about how much we gain i.e. profit or that we lose. So, firstly we should know that when we purchase or buy something by paying some amount of money, we refer that amount of money to be C.P. (COST PRICE) and the seller who sells that thing in some amount of money is called as S.P. (SELLING PRICE)
Complete step-by-step answer:
After this, we should know what profit and loss actually is. When S.P. (SELLING PRICE) is greater than C.P. (COST PRICE) then the shopkeeper will have Profit and if the C.P. (COST PRICE) is greater than S.P. (SELLING PRICE) then the shopkeeper will have Loss.
\[Profit = S.P - C.P\]
\[Loss = C.P - S.P\]
In terms of % , $profit\% = \dfrac{{S.P - C.P}}{{C.P}}X100$
And, \[loss\% = \dfrac{{C.P - S.P}}{{C.P}}X100\]
Complete step by step solution-
Given\[S.P. = Rs{\text{ }}605\], \[Gain{\text{ }}or{\text{ }}Profit{\text{ }}\% = 10\]
Let us calculate the C.P for that radio-set.
$Profit\% = \dfrac{{S.P - C.P}}{{C.P}}X100$
$10 = \dfrac{{605 - C.P}}{{C.P}}X100$
\[10 \times \left( {C.P} \right){\text{ }} = {\text{ }}\left( {605 - C.{\text{ }}P.} \right) \times 100\] ……by cross multiplying both sides
\[11 \times \left( {C.P} \right){\text{ }} = {\text{ }}605 \times 10\]
 $C.P. = \dfrac{{6050}}{{11}} = 550$
Hence, \[\left( {C.P} \right){\text{ }} = {\text{ }}Rs.{\text{ }}550\]
Now it is asking that for how much price (i.e. new S.P.) it should be sold to have gain% of \[16\% \]
$Profit\% = \dfrac{{S.P - C.P}}{{C.P}}X100$
$16 = \dfrac{{S.P - C.P}}{{C.P}}X100$
\[\;16 = \dfrac{{S.P - 550}}{{550}}X100\]
\[16 \times 550{\text{ }} = {\text{ }}\left( {S.P - 550} \right) \times 100\]
$S.P. - 550 = \dfrac{{8800}}{{100}}$
\[S.P. = 88 + 550\]
\[S.P. = 638\]
Hence, required \[{\mathbf{S}}.{\mathbf{P}}{\text{ }} = {\text{ }}{\mathbf{Rs}}.{\text{ }}{\mathbf{638}}\]
Note:
Either % should be converted into $\dfrac{1}{{100}}$ or for getting % we should multiply by\[100\].
The basic formula should be kept in mind i.e.
\[Profit = S.P - C.P\]
\[Loss = C.P - S.P\]