Question

Find the selling price if Cost price C.P. is 760 and loss percentage is $2\dfrac{1}{2}\%$.

Answer 1

Hint: To solve this problem we need to first know how to find the X% of a quantity Y. X% of the Y would be given as $X\%\,of\,Y\,=\dfrac{X}{100}\times Y$. So in this question first we will assume the selling price as X and then we will find the $2\dfrac{1}{2}\%$ of that amount and then add it with the total amount i.e. X. Now the obtained amount will be equal to the cost price from which we will find the value of X i.e. selling price.

Complete step by step answer:
We are given the cost price as 760 and loss percentage as $2\dfrac{1}{2}\%$ and we have to find the selling price of the product.
To solve this problem, we should know that what is the meaning of percentage,
Y% Percentage is defined as the Y parts per hundred parts of the given quantity.
And Y% of the Z amount is given by = $\dfrac{Y}{100}\times Z$
Now for this question we will first assume the selling price to be X,
So if we calculate the $2\dfrac{1}{2}\%$ of the amount X i.e. loss, we will get this as,
$\begin{align}
  & =2\dfrac{1}{2}\%\,of\,Rs.X \\
 & =\dfrac{5}{2}\%\,of\,Rs.X \\
 & =\dfrac{5}{2}\times \dfrac{1}{100}\times X \\
 & =\dfrac{1}{40}X \\
\end{align}$
Now we know that selling price is given as,
Selling price = cost price – loss
Selling price + loss = cost price
So we get,
$X+\dfrac{1}{40}X=720$
Taking the LCM we get,
$\begin{align}
  & \dfrac{40X+X}{40}=720 \\
 & \Rightarrow \dfrac{41X}{40}=720 \\
\end{align}$
Cross multiplying we get
\[\begin{align}
  & \Rightarrow X=\dfrac{40\times 720}{41} \\
 & \Rightarrow X=702.43 \\
\end{align}\]

Hence we get the required selling price as 702.43

Note: There is a mistake that a student might commit while solving this first is that when you are calculating the selling price, we are given a loss percentage then you might add it to the selling price instead of subtracting this would have been correct if we would have given gain percentage instead of loss percentage.