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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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2 Answers 2

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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 $$p=\frac{s-c}{s}.$$

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  • $\begingroup$ What is the final answer. Given ans is 50% $\endgroup$
    – user584736
    Aug 24, 2019 at 18:37
  • $\begingroup$ @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 $100\%.$ $\endgroup$
    – Allawonder
    Aug 24, 2019 at 19:00
  • $\begingroup$ Not getting the ans ... $\endgroup$
    – user584736
    Aug 24, 2019 at 19:01
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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,

$$m=\frac{1}{2}=50\%$$

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  • $\begingroup$ Ans given is 50 % not getting that ans $\endgroup$
    – user584736
    Aug 24, 2019 at 19:03
  • $\begingroup$ Thanks you for help $\endgroup$
    – user584736
    Aug 24, 2019 at 19:32

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