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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$\begingroup$ 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: math.meta.stackexchange.com/questions/5020/… $\endgroup$– Ethan BolkerAug 24, 2019 at 18:17
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2 Answers
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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 $$p=\frac{s-c}{s}.$$
answered Aug 24, 2019 at 18:18
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$\begingroup$ What is the final answer. Given ans is 50% $\endgroup$ Aug 24, 2019 at 18:37
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$\begingroup$ @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 $100\%.$ $\endgroup$ Aug 24, 2019 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,
$$m=\frac{1}{2}=50\%$$
