There are several ways business arithmetic can be managed using short cuts. Two of the most common, mark downs and mark ups, are outlined below.
The first we will discuss is discount, or mark-down. Retail stores figure the discount they get from the manufacturer or wholesaler with the retail price as the base (book stores, hardware stores, most specialized stores) or - just the opposite in some fields - with the net, discounted price as the base (department stores, chain stores, etc.). When the net price is the base, the store figures mark on or mark up, rather than mark down.
The difference becomes clear in a concrete example.
Mark-down
Suppose a lawn mower retailing for $150 comes to the store with a 30% discount. What is the net price to the store?
The base here is $150. Change the percentage to a decimal and simply multiply. The discount in dollars is .30 times $150, or $45. The net price is $150 minus $45, or $105.
Short cut: The quickest way to figure a net price is not to work out the discount in dollars and then subtract, but to mentally convert the discount into its complement (of 100) and multiply the retail price directly by this. If the retailer gets a 30% discount, then he naturally pays 70% of the retail price.
.70 x $150 gives $105 in one operation, without subtracting.
Try one yourself. A typewriter with a list price of $85 carries a 15% discount to the store. What does the retailer pay for it?
The standard way of doing this is to take .15 of $85, or $12.75, and deduct this from $85 to get a net price of $72.25. The short way is to note that the dealer, in getting a 15% discount, pays 85% of the retail price. So we multiply .85 x $85 and, again, get $72.25 in one operation.
Mark-up
The opposite expression used in many fields is to begin with the net price (the discounted price to the dealer) and arrive at a desired selling price by deciding how much mark-up is required.
A store might have a desired 20% mark-up, for instance. If it buys baby carriages at $30 each net, how much should it sell them for?
Mark-up is figured with the net price as the base, rather than the retail price, so 20% of $30 is $6.00. Adding the cost and the mark-up, the store will sell its baby carriages for $36.
Once again, this can be done without adding, in one operation, by considering that adding 20% to the net price is the same as multiplying the net price by 120%. In this case the short cut is not so effective, however, since you add in the process of multiplying anyway.
Work out a proper selling price for an article that costs $47 and should deliver a 40% mark-up to the store.
For this calculation 40% becomes .4, and .4 x $47 is $18.80. Adding $18.80 to $47, we find a desired retail price of $65.80.
Using the above method, you should arrive at your answer much more quickly than using the conventional methods.
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