A man bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for $$\$ 55$$ more, he would have a profit of 40%. Find the CP of the article.

Question

Vedantu Content Team · Accepted Answer

Hint: First find the SP when the article is sold at a 10% loss then find the cost price when the article is bought is 20% less after this add 55 to the last obtained SP to get a new SP on which man gets a profit of 40%. Use new CP, SP, and 40% to form an equation by using the formula of profit percentage.Complete step-by-step answer:We have to find the cost price so let’s suppose it is $$x$$.Now first we will consider the first statement that is “A man bought an article and sold it at a loss of 10%” and will find SP.We know the formula of loss percentage that is $${\text{loss}}\% = \dfrac{{CP - SP}}{{CP}} \times 100\% $$.Now we will substitute $$x$$ for CP and 10 for loss percent and will find the value for SP,$$10 = \dfrac{{x - SP}}{x} \times 100$$$$\Rightarrow \dfrac{{10}}{{100}} = \dfrac{{x - SP}}{x}$$$$\Rightarrow 0.1 = \dfrac{{x - SP}}{x}$$Cross Multiply and evaluate SP$$0.1x = x - SP$$$$\Rightarrow 0.1 - x = - SP$$$$\Rightarrow - 0.9x = - SP$$$$\Rightarrow 0.9x = SP$$$$\Rightarrow SP = 0.9x$$From this, we get the selling price of the article when the man bought an article and sold it at a loss of 10%Now we know that person bought the article for 20% less, by using this statement we will find the cost price $$CP'$$ and for this, we will subtract 20% of CP from the cost price.$$CP' = x - \dfrac{{20}}{{100}}x$$$$CP' = x - 0.2x$$$$CP' = 0.8x$$Now we know that if the person bought the article for 20% less then he sold it for $$\$ 55$$ more, by using this statement we will find the cost price $$SP'$$ and for this we will add $$\$ 55$$ to the obtained SP.$$SP' = SP + 55$$$$SP' = 0.9x + 55$$Now we know that if the person bought the article in $$CP' = 0.8x$$ and sold it in $$SP' = 0.9x + 55$$ then he has a profit of 40%.We will use this information into the profit formula $${\text{Profit}}\% = \dfrac{{SP - CP}}{{CP}} \times 100\% $$to get an equation.Substituting the values into the formula, $$40 = \dfrac{{\left( {0.9x + 55} \right) - 0.8x}}{{0.8x}} \times 100$$Now we will solve this equation for x,$$40 = \dfrac{{0.9x + 55 - 0.8x}}{{0.8x}} \times 100$$$$\Rightarrow \dfrac{{40}}{{100}} = \dfrac{{0.1x + 55}}{{0.8x}}$$$$\Rightarrow 0.4 = \dfrac{{0.1x + 55}}{{0.8x}}$$Cross Multiply and evaluate the value of $x$.$$0.4 \times 0.8x = 0.1x + 55$$$$\Rightarrow 0.32x = 0.1x + 55$$$$\Rightarrow 0.32x - 0.1x = 55$$$$\Rightarrow 0.22x = 55$$$$\Rightarrow x = \dfrac{{55}}{{0.22}}$$$$\Rightarrow x = 250$$Thus, the cost price is $$\$ 250$$.Note: The last profit which is 40% will be computed on new CP and new SP as the statement is “If he had bought it for 20% less and sold it for $$\$ 55$$ more, he would have a profit of 40%”.

A man bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for \[\$ 55\] more, he would have a profit of 40%. Find the CP of the article.