Question

Selling price of a toy car is $Rs540$. If the profit made by the shopkeeper is $20\% $, what is the cost price of the toy?

Answer 1

Hint:In order to solve such a problem, assume the cost price of the toy to be a variable. Then form the equation by using that profit $ = 20\% $ between the cost price and the selling price. At last solve the equation to get the answer.

Complete step-by-step answer:
Let us assume that the cost price of the toy be $Rs{\text{ }}x$
Before moving ahead let us know what the cost price and the selling price is. Cost price is the price of the object at which the shopkeeper bought it and the selling price is the price at which the shopkeeper sold it to the customer which means the price at which the customer bought it from the shopkeeper.
${\text{profit/loss}} = \dfrac{{\left| {{\text{selling price - cost price}}} \right|}}{{{\text{cost price}}}} \times 100$
Now as given that the selling price of the toy is $Rs540$
Next it is said in the question that the shopkeeper had the profit of $20\% $
This means that the selling price of the toy is greater than its cost price which means that $x < 540$
Now we are given that
$CP = Rs{\text{ }}x$ and $SP = Rs{\text{ 540}}$
Using these values in the formula, we get that
${\text{profit}} = \dfrac{{({\text{selling price - cost price)}}}}{{{\text{cost price}}}} \times 100$
$20 = \dfrac{{540 - x}}{x} \times 100$
$540 - x = \dfrac{{20x}}{{100}}$
$540 - x = \dfrac{x}{5}$
$540 = x + \dfrac{x}{5}$
$540 = \dfrac{{6x}}{5}$
$x = \dfrac{{540(5)}}{6} = 450$
Hence the cost price of the toy is $Rs450$

Note: If the selling price > cost price
Then it will be the profit
${\text{profit}} = \dfrac{{({\text{selling price - cost price)}}}}{{{\text{cost price}}}} \times 100$
If the selling price < cost price
Then it will be the loss
${\text{loss}} = \dfrac{{({\text{ cost price - selling price )}}}}{{{\text{cost price}}}} \times 100$
And the important point is that these profits and loss are with respect to the shopkeeper