Percentage profit-loss

Question

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?

Answer 1

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

Answer 2

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,

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