Question

Selling price of a toy is $Rs.540$ . If the profit made by the shopkeeper is $20\% $ , what is the cost price of this toy?

Answer 1

Hint: Remember that the profit percentage is calculated by dividing the difference between SP and CP with CP. So use this relation to form an equation with one unknown, i.e. CP. It can be written as ${\text{Profit}}{\text{% = }}\dfrac{{SP - CP}}{{CP}} \times 100$ . Substitute all the values and solve for the value of cost price

Complete step-by-step answer:
In this problem, we are given the selling price of a toy and the percentage profit made by a shopkeeper after selling. With these two given data, we need to find out the cost price of the toy.
Let’s first understand the concept of profit. Profit is an amount earned by selling an item at a price more than the cost price of the item. Profit is the difference in the selling price of a commodity with its cost price when the selling price is more than the cost price. This will give us the expression:
$ \Rightarrow {\text{Profit }} = {\text{ }}SP - CP$ and ${\text{Profit}}{\text{% = }}\dfrac{{SP - CP}}{{CP}} \times 100$ (i)
So here we have data ${\text{Profit% }} = 20\% $ and $SP = Rs.540$
Now, we substitute the above values in the relation (i), we get:
$ \Rightarrow 20 = \dfrac{{540 - CP}}{{CP}} \times 100$
We can solve this equation to find the value of CP by first dividing both sides with $100$
$ \Rightarrow \dfrac{{20}}{{100}} = \dfrac{{540 - CP}}{{CP}} \times \dfrac{{100}}{{100}} \Rightarrow \dfrac{1}{5} = \dfrac{{540 - CP}}{{CP}}$
After changing the fraction by transposing CP from the denominator to LHS, we get:
$ \Rightarrow \dfrac{1}{5} = \dfrac{{540 - CP}}{{CP}} \Rightarrow CP = 5\left( {540 - CP} \right)$
Now we can bring the terms with CP on one side and solve it for the value of CP as:
$ \Rightarrow CP = 5\left( {540 - CP} \right) \Rightarrow CP + 5CP = 540 \times 5 \Rightarrow 6CP = 2700 \Rightarrow CP = \dfrac{{2700}}{6} = 450$
Therefore, we got the value of $CP = Rs.450$
Hence, the cost price of the required toy as $Rs.450$

Note: Be careful while substituting the value profit percentage, it should be written as $20$ not as $\dfrac{{20}}{{100}}$ in the relation (i). Do confuse with the equation ${\text{Profit }} = {\text{ }}SP - CP$ and ${\text{Profit}}{\text{% = }}\dfrac{{SP - CP}}{{CP}} \times 100$ because given data is of profit percentage not of profit.
An alternative approach can be taken by changing equation ${\text{Profit}}{\text{% = }}\dfrac{{SP - CP}}{{CP}} \times 100$ before substitution into ${\text{Profit}}{\text{% = }}\left( {\dfrac{{SP}}{{CP}} - 1} \right) \times 100 \Rightarrow 100 + {\text{Profit% }} = \dfrac{{SP}}{{CP}} \times 100$ . Now if you will substitute values in this new equation, it will be easier for calculations.