Question

By selling a sofa-set for Rs2500, the shopkeeper loses 20%. Find his loss percent or profit percent, if he sells the same sofa-set for Rs3150.

Answer 1

Hint: The selling price of the sofa should be equal to the cost price of the sofa subtracted the less suffered by him on the cost price. Hence take the cost price of the sofa to be a variable and form a linear equation involving this variable using the above concept.

Complete Step-by-Step solution:
Let the cost price of the sofa be x Rs.
Now it is given that the shopkeeper sells the sofa set at Rs. 2500 so the shopkeeper loses 20%.
So construct the linear equation according to given information we have,
Therefore cost price of sofa-set – 20% of cost price of sofa-set is equal to Rs. 2500
$ \Rightarrow x - \dfrac{{20}}{{100}}x = 2500$
Now simplify the above equation we have,
$
   \Rightarrow x - \dfrac{1}{5}x = 2500 \\
   \Rightarrow \dfrac{{4x}}{5} = 2500 \\
 $
$ \Rightarrow x = \dfrac{{2500 \times 5}}{4} = 3125$ Rs.
So the cost price of sofa-set is Rs. 3125.
Now he sells the sofa-set for Rs. 3150.
Now it is clear that the selling price is greater than the cost price so the shopkeeper earns the profit.
Therefore the profit (P) earned by the shopkeeper = selling price – cost price.
$ \Rightarrow P = 3150 - 3125 = 25$ Rs.
So the profit percentage is the ratio of profit to cost price multiplied by 100.
$ \Rightarrow P = \dfrac{{25}}{{3125}} \times 100 = 0.8$ %
So this is the required profit percentage.

Note: Whenever we face such type of problems the key concept is to have understanding about the selling price and cost price of the product, the price at which the product is sold to the customer is the selling price whereas the cost price is the cost at which the product is made available to the seller himself. Use the relation between them to get the answer for such types of problems.