Question

A salesman has the liberty to sell a hair dryer in his store at a price between $ Rs.300 $ and $ Rs.700 $ . Profit earned by selling the hair dryer for $ Rs.650 $ is twice the loss incurred when it is sold for $ Rs.350 $ . What is the cost price of the hair dryer?

Answer 1

Hint: In order to calculate the cost price of the hair dryer, obtain an equation from the information given, that the profit obtained by selling the hair dryer for $ Rs.650 $ is twice the loss incurred when it is sold for $ Rs.350 $ . Just substitute the values in the equation, equate them and get the value of the cost price of the hair dryer.

Complete step by step solution:
We know that profit earned when selling is greater than the cost price, it is nothing but the difference between selling price and cost price.
So, according to that the equation for profit is $ profit = sp - cp $ , where $ sp $ stands for selling price and $ cp $ stands for cost price.
Similarly, loss is earned when the selling price is less than the cost price, it is nothing but the difference between cost price and selling price.
So, according to that the equation for loss is $ loss = cp - sp $ .
According to question:
Selling price when there is a chance of profit is $ Rs.650 $ , that means $ sp = Rs.650 $ . Substituting it in the profit equation, we get:
 $
  profit = sp - cp \\
  profit = 650 - cp \;
  $
Now, when the salesman sells the hair dryer at $ Rs.350 $ , there is a loss, that means $ sp = Rs.350 $ . Substituting it in the loss equation, we get:
 $
  loss = cp - sp \\
  loss = cp - 350 \;
  $
It’s given that the profit made is twice of the loss, in equation it is written as:
 $ profit = 2\left( {loss} \right) $
Substituting the value of $ sp $ and $ cp $ in the above equation, we get:
 $
  profit = 2\left( {loss} \right) \\
  sp - cp = 2\left( {cp - sp} \right) \\
  650 - cp = 2\left( {cp - 350} \right) \;
  $
Further solving for $ cp $ :
 $
  650 - cp = 2\left( {cp - 350} \right) \\
  650 - cp = 2cp - 700 \\
   - cp - 2cp = - 700 - 650 \\
   - 3cp = - 1350 \\
  \dfrac{{ - 3cp}}{{ - 3}} = \dfrac{{ - 1350}}{{ - 3}} \\
  cp = 450 \;
  $
And, hence $ cp $ obtained is $ Rs.450 $ .
Therefore, the cost price of the hair dryer is $ Rs.450 $ .
So, the correct answer is “ $ Rs.450 $ ”.

Note: The selling price in profit and loss equations are given separately for the question (one for loss and other for profit), do not take it for one selling price.
We can also find the profit or loss percent by dividing the loss and profit by cost price and multiplying it by hundred, that is:
 $
  profit\% = \dfrac{{profit}}{{cp}} \times 100\% \\
  loss\% = \dfrac{{loss}}{{cp}} \times 100\% \;
  $