Word Problem 1 (Profit calculation on marked price basis)

Problem 1: How much percent a tradesman increase on to the cost price to his goods so that he may make a net profit of 10% after allowing a customer a discount of 4% of his bill ?

a. 14-7/12%            b. 16-1/2%                        c. 20%                    d. 19-1/2%

(word problems on job exam mathematics.)


We suppose her that Cost Price is ‘y’

i-e CP=y

First we will calculate Selling Price SP by using Profit formula

We know that;

Profit = Selling Price- Cost Price



But Profit is 10% of cost price i-e


Put values in above relation

\Rightarrow \frac{10y}{100}=SP-y

\Rightarrow SP= \frac{110y}{100}

This is selling price !

Now we will calculate Marked Price MP using Discount formula;

Formula for Discount percentage is ;

Discount%= \frac{Marked Price -Selling Price}{Marked Price}\times100

in short we write

Discount%= \frac{MP -SP}{MP}\times100

Now discount %age is given to be 4%


\Rightarrow 4= \frac{MP -SP}{MP}\times100

\Rightarrow 4MP= 100MP -100SP

\Rightarrow MP= \frac{100}{96}\times SP

But We have calculated above


Put value;

\Rightarrow MP=\frac{100}{96}\times\frac{110y}{100}

\Rightarrow MP=\frac{110y}{96}

This is marked price !

Now finally we can calculate sought increase in Cost Price CP using formula

Increase Over CP= \frac{Marked Price - Cost Price}{Cost Price}\times 100

Increase Over CP= \frac{MP - CP}{C P}\times 100

Putting values of MP and CP and simplifying

\Rightarrow Increase Over CP=\frac{110y-96y}{96y}\times100

\Rightarrow Increase Over CP=\frac{14y}{96y}\times100

\Rightarrow Increase Over CP=14\frac{7}{12}%

So the option ‘a’ is correct


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