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She sells a dress for $42.60 after making a profit of 20 percent on the cost price. Calculate the cost price.

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Last updated date: 25th Feb 2024
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IVSAT 2024
Answer
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Hint: Now we are given the selling price and profit percentage. Let us assume the cost price to be x. We know that profit is given by selling price – cost price and the profit percentage is given by $\dfrac{\text{profit}}{\text{cost price}}\times 100$ . Hence we will use these equations to find the value of x and hence we will find the cost price of the dress.

Complete step by step answer:
Now we are given that the selling price of the dress is 42.60 and the profit percentage is 20.
We want to find the cost price of the dress. Let us assume that the cost price of the dress is x.
Now we know that the profit is given by cost price – selling price.
Hence profit = x – 42.60.
Now we know that the profit percentage is given by $\dfrac{\text{profit}}{\text{cost price}}\times 100$ .
Now substituting the values in the equation we get, $\dfrac{x-42.60}{x}\times 100=20$
Now multiplying the equation by x we get, $100\left( x-42.60 \right)=20x$
Now dividing the whole equation by 20.
\[\Rightarrow 5\left( x-42.60 \right)=x\]
Opening the bracket we get,
\[\Rightarrow 5x-213=x\]
Let us rearrange the terms to solve the equation.
\[\begin{align}
  & \Rightarrow 5x-x=213 \\
 & \Rightarrow 4x=213 \\
\end{align}\]
Now dividing the whole equation by 4 we get,
$x=\dfrac{213}{4}=53.25$
Hence the cost price of the dress was $53.25.

Note: Now note that if cost price is more than selling price then we say that it was a loss and hence in this case loss will be given cost price – selling price. Also to find the loss percentage we will use the formula $\dfrac{\text{loss}}{\text{cost price}}\times 100$ .
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