Question

A dealer earned a profit of $5\% $ by selling a radio for ${\text{Rs}}{\text{.714}}$ . Find the cost price of the radio?

Answer 1

Hint:In the question they have given the selling price and profit percentage and then ask us to find the cost price of the radio. We can use the profit percentage formula to solve it. In profit, the selling price should be greater than the cost price and in loss, the cost price should be greater than the selling price.

Formula used:The formula used for this question is,
 ${\text{Profit}}\% = \dfrac{{{\text{Profit}}}}{{{\text{CP}}}} \times 100$
 ${\text{Profit}} = {\text{SP}} - {\text{CP}}$
Where,
 ${\text{CP}}$ is the Cost price
 ${\text{SP}}$ is the Selling price

Complete step-by-step answer:
The data given in the question are,
The selling price of radio after selling the radio is ${\text{Rs}}{\text{.714}}$
The profit percentage after selling the radio = $5\% $
 Let the cost price of the radio be ${\text{x}}$ ,
Substitute the values in the profit percentage formula,
 ${\text{Profit}}\% = \dfrac{{{\text{Selling Price - Cost Price}}}}{{{\text{CP}}}} \times 100$
 $5 = \dfrac{{714 - {\text{x}}}}{{\text{x}}} \times 100$
While solving the above we get,
 $5{\text{x}} = (714 - {\text{x}}) \times 100$
Simplifying the above we get,
 ${\text{5x}} = 71400 - 100{\text{x}}$
Bringing the ${\text{x}}$terms on one side we get,
 ${\text{5x + }}100{\text{x}} = 71400$
By solving the above we get,
 $105{\text{x}} = 71400$
At last the value of ${\text{x}}$ will be,
 ${\text{x}} = \dfrac{{71400}}{{105}}$
By cancelling the above we get,
 ${\text{x}} = 680$
 $\therefore $ The cost price of the radio is \[680\,{\text{rupees}}\].
Hence, the cost price of the radio is \[680\,{\text{rupees}}\].

So, the correct answer is “Option A”.

Note:We have to notice whether the cost is given in which unit, example: rupees, paisa etc… if they have given loss then we have to proceed the solution according to it by using the loss formula which is given by ${\text{Loss}}\% = \dfrac{{{\text{Cost Price-Selling Price }}}}{{{\text{CP}}}} \times 100$.