1. ## Mathematics of merchandising

Hi all, I'm having a really tough time with this question... a little guidance?

30% markup of cost price..then 58% discount off selling price. What percent is the resulting profit or loss on this sale?

So i have that selling price = cost + markup = 100 + 30 = 130 %
now what?

Thanks..I'm so lost.

2. Originally Posted by clarke915
Hi all, I'm having a really tough time with this question... a little guidance?

30% markup of cost price..then 58% discount off selling price. What percent is the resulting profit or loss on this sale?

So i have that selling price = cost + markup = 100 + 30 = 130 %
now what?

Thanks..I'm so lost.
Let cost price be P. Then P --> P + 30% of P = 1.3P --> 1.3P - 58% of 1.3P = 1.3P - 0.58(1.3P) = 1.3P - 0.754P = 0.546P.

So there is a loss of (100 - 54.6)% = 45.4%.

3. 1 - (1 + .30)(1 - .58)
= 1 - 1.3(.42)
= 1 - .546
= .454 or 45.4%

If you wanna see that "in action", assume \$100 as cost price:

30% of 100 = 100 * .30 = 30;
so selling price = 100 + 30 = 130 ; ok?

58% of 130 = 130 * .58 = 75.40;
so price after discount = 130 - 75.40 = 54.60 ; still with me?

Results in net loss of 100 - 54.60 = 45.4, or 45.4% ; kapish?