Question

By selling a table for Rs. 330, a trader gains \[10\% \]. Find the cost price of the table.

Answer 1

Hint: Here, we are required to find the cost price of a table whose selling price and profit percentage is given. We will use the formula of selling price when an item is sold at profit to find the value of its cost price. Substituting the given values in the formula will give us the required value of Cost Price.

Complete step-by-step answer:
According to the question, it is given that:
Selling Price of a table, S.P. \[ = \]Rs. 330
Gain percentage\[ = \]\[10\% \]
We are required to find the Cost Price, i.e. C.P.
Now, as we know,
S.P.\[ = \](100\[ + \]Gain\[\% \]/100)\[ \times \]C.P.
Now, substituting the given values of S.P. and gain percentage in this formula, we get,
$\Rightarrow$ \[330 = \dfrac{{100 + 10}}{{100}} \times \]C.P.
$\Rightarrow$ \[330 = \dfrac{{110}}{{100}} \times \]C.P.
Or
$\Rightarrow$ \[330 = \dfrac{{11}}{{10}} \times \]C.P.
Multiplying both sides by 10,
$\Rightarrow$ \[330 \times 10 = 11 \times \]C.P.
We can write this as:
$\Rightarrow$ \[3300 = 11 \times \]C.P.
Divide both sides by 11,
$\Rightarrow$ \[\dfrac{{3300}}{{11}} = \]C.P.
Hence, C.P. \[ = 300\]
Therefore, the cost price of the table is Rs. 300
Hence, this is the required answer.

Note: For solving this question, it is really important to know the difference between Cost Price and Selling Price.
In simple terms, Cost Price is the amount at which the retailer/seller has bought the product i.e. the total cost at which the product has been made.
And Selling Price is the amount at which the buyer/customer is willing to purchase that product.
Now, if the C.P. is greater than the S.P then it is a loss for the seller but if the S.P is greater than the CP then it is a profit.
Therefore, if we add the amount of profit earned to the Cost Price then, we get the Selling Price.
Hence, the formula of S.P. is:
S.P.\[ = \](100\[ + \]Gain\[\% \]/100)\[ \times \]C.P.
Substituting the given values in this formula helped us to find the required value of the Cost Price.