Question

The selling price of a toy car is Rs540. If the profit made by the shopkeeper is 20%, what is the cost price of this toy?

Answer 1

Hint: First, assume the cost price of the car. Then find the profit made by the shopkeeper. After that substitute the values in the profit percent formula, \[Profit\%=\dfrac{Profit}{Cost\,Price}\times 100\]. Then solve it to get the cost price of the car.

Complete step by step answer:
Given: - Selling price of toy car = Rs. 540
Profit percent = 20%
Let the cost price of the toy be Rs. $x$.
Since the shopkeeper made a profit. Then,
Profit = Selling Price - Cost price
Substitute the values,
Profit = 540 - $x$
The formula of profit percent is given by,
\[Profit\%=\dfrac{Profit}{Cost\,Price}\times 100\]
Substitute the values in the above formula,
$\Rightarrow 20=\dfrac{540-x}{x}\times 100$
Cross multiply the terms,
$\Rightarrow 20x=54000-100x$
Move the variable part on the left side,
$\Rightarrow 120x=54000$
Divide both sides by 120,
$\Rightarrow x=450$
Hence, the cost price of the car is Rs. 450.

Note:
Cost price (CP) is the price at which an article is purchased.
Selling price (SP) is the price at which an article is sold.
If the selling price is more than the cost price, profit(gain) occurs.
Profit = Selling Price - Cost price
If the selling price is less than the cost price, loss occurs.
Loss = Cost Price - Selling Price
The formula for calculating the profit percent is,
\[Profit\%=\dfrac{Profit}{Cost\,Price}\times 100\]
The formula for calculating the loss percent is,
\[Loss\%=\dfrac{Loss}{Cost\,Price}\times 100\]