Question

A person by selling an article at half of the retail price incurs him a loss of 30%.find the profit percentage if he sells at the list price?

Answer 1

Answer:

The profit percentage is 40% if he sells at the list price.

Answer 2

Given:

A person by selling an article at half of the retail price incurs him a loss of 30%

To Find:

find the profit percentage if he sells at the list price?

Solution:

It is given that a person sells an article at half the retail price ( retail price here means the marked price of the article) and incurs a loss of 30%, now we need to find the profit percentage if he sells the article at the listed price, for that first we will need to find the cost price of the article,

Let the Marked price of the article be x, so the selling price in the first will become x/2, now applying the formula for loss percentage, we have

$loss\%=\frac{CP-SP}{CP}*100\\30=\frac{CP-\frac{x}{2} }{CP} *100\\3CP=10CP-5x\\CP=\frac{5x}{7}$

So now we have the value for the cost price of the article, now we need to find the profit percentage if the article is sold at the listed price, then selling price will be equal to x, applying in the formula, we have

$profit\%=\frac{SP-CP}{CP}*100\\=\frac{x-\frac{5x}{7} }{\frac{5x}{7} } *100\\=\frac{2x}{5x} *100\\=40\%$

Hence, the profit percentage, if he sells the article at the listed price, will be 40%.