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# The list price of a table fan is Rs 480 and it is available to a retailer at $25\%$ discount. For how much should a retailer sell it to gain $15\%$?

Last updated date: 15th Jul 2024
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Hint: The question is related to the discount topic. Here they have mentioned the discount percentage by using the formula $discount\% \, = \,\dfrac{{discount}}{{M.P}} \times 100\%$, we determine the value of discount. Then by using the formula $C.P = \,M.P - discount$, we determine the value of cost price. Then by using the formula $gain\% \, = \,\dfrac{{S.P - C.P}}{{C.P}} \times 100\%$, we determine the selling price.

Complete step by step solution:
Now we go through the question and we solve it.
The list price of a table is Rs. 480. The list price is also called the marked price.
The marked price of a table fan = Rs.480
The discount percent on the table = $25\%$
By using formula $discount\% \, = \,\dfrac{{discount}}{{M.P}} \times 100\%$, we determine the value of discount.
On substituting the values.
$\Rightarrow 25\% \, = \,\dfrac{{discount}}{{480}} \times 100\%$
On rewriting this we have
$\Rightarrow discount = \dfrac{{25 \times 480}}{{100}}\,$
On simplifying we have
$\Rightarrow discount = 120$
Therefore the discount is Rs. 120
The retailer one you purchase the thing and he sells to the public.
So he will buy the table fan. Then the cost price of the table fan will be determined using the formula $C.P = \,M.P - discount$, on substituting the values we have
$\Rightarrow C.P = \,480 - 120$
On simplifying we have
$\Rightarrow C.P = \,360$
Therefore the retailer will buy the table fan for Rs. 360
When the retailer sells the table fan to the public he will get the profit $15\%$, so by considering this we have to determine the value of selling price.
First we determine the value of profit or gain then we determine the selling price.
By using the formula $gain\% \, = \,\dfrac{{gain}}{{C.P}} \times 100\%$
On substituting the values we have
$\Rightarrow 15\% \, = \,\dfrac{{gain}}{{360}} \times 100\%$
On rearranging this can be written as
$\Rightarrow gain = \dfrac{{15 \times 360\,}}{{100}}$
On simplifying we get
$\Rightarrow gain = 54$
Therefore the retailer will get the Rs.54 as a profit.
Now we have to determine the selling price of a table fan where the retailer sold.
We use the formula $gain = S.P - C.P$
Substituting the values we get
$\Rightarrow 54 = S.P - 360$
Take 360 to LHS we get
$\Rightarrow 54 + 360 = S.P$
On adding 360 and 54 we get
$\Rightarrow S.P = 414$
Therefore the retailer sold the table fan at Rs.414
So, the correct answer is “Rs.414”.

Note: Here in this we came across two topics that are discount and profit & loss. The question is a little bit twisty, in the question they have mentioned the word retailer. Where retailer means the person who buys a thing and he will sell to the public. So for that we will come across two topics. For simplification we have to know the simple arithmetic operations and the tables of multiplication.