Question

On selling computers for\[Rs.24480\], a dealer loses \[4\% \]. For how much should he sell it to gain \[4\% \]?

Answer 1

Hint: Here, we will find the cost price of computers by using the selling price in terms of the loss percentage. Then we will substitute the obtained cost price and fain percentage in the formula of selling price to find the selling price.

Formula used:
We will use the following formula:
1.Selling price is given by the formula \[S.P. = \left( {\dfrac{{100 + {\rm{Gain}}\% }}{{100}}} \right) \times C.P.\]
2.Selling price is given by the formula \[S.P. = \left( {\dfrac{{100 - {\rm{Loss}}\% }}{{100}}} \right) \times C.P.\]

Complete step-by-step answer:
Let \[x\] be the Cost Price of Computers.
We are given that on selling computers for \[{\rm{Rs}}.24480\], a dealer loses \[4\% \].
Now, we will find the cost price of computers by using the selling price formula in terms of loss percentage.
Selling Price of Computers \[ = \left( {\dfrac{{100 - {\rm{Loss}}\% }}{{100}}} \right) \times C.P.\]
By substituting the selling price of computers and loss percentage in the above equation, we get, we get
\[ \Rightarrow 24480 = \left( {\dfrac{{100 - 4}}{{100}}} \right) \times x\]
By subtracting the terms, we get
\[ \Rightarrow 24480 = \left( {\dfrac{{96}}{{100}}} \right) \times x\]
By simplifying the terms, we get
\[ \Rightarrow 24480 = \left( {\dfrac{{24}}{{25}}} \right) \times x\]
By rewriting the equation, we get
\[ \Rightarrow x = 24480 \times \left( {\dfrac{{25}}{{24}}} \right)\]
Multiplying the terms, we get
\[ \Rightarrow x = {\rm{Rs}}.25,500\]
Thus, the cost price of computers is \[{\rm{Rs}}.25,500\]
Now, we will find the selling price of computers by using the selling price in terms of profit percentage.
Selling Price of Computers \[ = \left( {\dfrac{{100 + {\rm{Gain}}\% }}{{100}}} \right) \times C.P.\]
By substituting the gain percentage and the cost price of computers in the above equation, we get
\[ \Rightarrow \] Selling Price of Computers \[ = \left( {\dfrac{{100 + 4}}{{100}}} \right) \times 25500\]
By adding the terms, we get
\[ \Rightarrow \] Selling Price of Computers \[ = \left( {\dfrac{{104}}{{100}}} \right) \times 25500\]
By simplifying the terms, we get
\[ \Rightarrow \] Selling Price of Computers \[ = 104 \times 255\]
By multiplying the terms, we get
\[ \Rightarrow \] Selling Price of Computers \[ = {\rm{Rs}}.26,775\]
Therefore, the Selling Price of Computers is \[{\rm{Rs}}.26,775\].

Note: We know that the cost price is the price of an item at which an item is bought. The selling price is the price of an item at which an item is sold. If the selling price is greater than the cost price, then there is a profit. If the selling price is less than the cost price, then there is a loss. Profit or loss percentage is calculated only for the same number of items. Both the percentages are calculated over the cost price of an item.