Question

A man bought an article for Rs x and sold it for Rs 16. If his loss was x percent, find the cost price of the article.

Answer 1

Hint: Convert the statement into an equation to solve it. According to the question you need to calculate loss as required in the loss percent formula .Then using the formula calculate the cost price of the article.

Formula used:
 Here, we use the formula of loss percent = \[\dfrac{{Loss}}{{C.P}} \times 100\] and loss = \[C.P - S.P\]

Complete step-by-step answer:
 Let C.P be the cost price of the article which means \[C.P{\rm{ }} = {\rm{ }}xRs.\] and S.P be the selling price of the article which means \[S.P{\rm{ }} = {\rm{ 16}}Rs.\]
Now, we will calculate loss as in the question we have been given loss percent.
So, we use the formula of loss = \[C.P - S.P\] .
As we have both the value i.e C.P and S.P,
Therefore, loss = \[\left( {x - 16} \right)Rs\]
So, now we will calculate the Cost price of percent using the formula loss percent = \[\dfrac{{Loss}}{{C.P}} \times 100\].
As, we have all the values i.e loss and C.P and loss percent is given that is x percent.
So, by substituting all the values we get,
$\Rightarrow$ \[x = \dfrac{{\left( {x - 16} \right)}}{x} \times 100\]
Here, we will simplify right hand side which comes out to be:
$\Rightarrow$ \[x = \dfrac{{100x - 1600}}{x}\]
By cross multiplication we get,
$\Rightarrow$ \[{x^2} = 100x - 1600\]
Taking all the values on left hand side we get,
$\Rightarrow$ \[{x^2} - 100x + 1600 = 0\]
Here, we will calculate the factors by using factorization that is:
$\Rightarrow$ \[{x^2} - 80x - 20x + 1600 = 0\]
Taking out all the common values,
$\Rightarrow$ \[x\left( {x - 80} \right) - 20\left( {x - 80} \right) = 0\]
By, combining all the values
$\Rightarrow$ \[\left( {x - 80} \right)\left( {x - 20} \right) = 0\]
So, from above equation x comes out to be \[x = 80,20\] which means the cost of the article can be 20 Rs. Or 80 Rs.

Note: In these types of questions check what is given and then convert that given part into equations. Then use the formula according to the values that are given. Here, the above question is of loss, similarly the question can be of profit.