If the discount given is equal to 25% of the selling price and the sale gives the trader a profit of 50/3 % when calculated on his selling price, by what percent did he mark up the cost price before offering the discount?
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Welcome to stackexchange. You are more likely to get help rather than downvotes and votes to close if you [edit] the question to show us what you tried and where you are stuck. Use mathjax: https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference – Ethan Bolker Aug 24 '19 at 18:17
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Let the markup percent be $p,$ and the cost and selling prices respectively be $c$ and $s.$ Then we have that $$(1+p)c=s.$$ Also, we know that the superficial profit is $pc,$ out if which we must subtract the discount $0.25s$ in other to get the true profit $s/6.$ Thus, we get that $$s/6=pc-0.25s.$$ Finally, recall that $$p=\frac{s-c}{s}.$$
Allawonder
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@user584736 Have you tried to solve for $p$ as given by the system I defined? What difficulty did you encounter. Note that to change the calculated value of $p$ to a percentage, multiply by $100%.$ – Allawonder Aug 24 '19 at 19:00
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Let cost $c$, sales $s$ and the markup $m$. From the markup and discount statements,
$$c(1+m)=s(1+25\%)\tag{1}$$
and from the profit statement,
$$\frac{s-c}{s}=\frac{50}{3}\%\tag{2}$$
Obtain $c/s=5/6$ from (2) and plug it into (1) to get the markup,
$$m=\frac{1}{2}=50\%$$
Quanto
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