2.3 Percentages: increase/decrease, discounts, markups, tax, commissions, defect rates

Percentages in the Workplace

"Percent" means "per hundred," so 25% = 25/100 = 0.25. Nearly every percentage problem on the test becomes easy once you convert the percent to a decimal and remember one core idea: percent of a number = decimal x number.

Finding a Percent of a Number

Example. A store expects 8% of its 2,500 daily visitors to make a purchase. 8% = 0.08, so 0.08 x 2,500 = 200 buyers.

Example. A crew has completed 65% of a 3,200-foot pipeline. 0.65 x 3,200 = 2,080 feet finished.

Sales Tax

Sales tax is a percent added to the price. Compute the tax, then add it.

Example. A tool costs $85.00 and sales tax is 7%. Tax = 0.07 x $85.00 = $5.95. Total = $85.00 + $5.95 = $90.95.

A shortcut: multiply by 1.07 - that is "the whole price plus 7% more": $85.00 x 1.07 = $90.95. Same answer, one step.

Discounts and Sale Price

A discount is a percent subtracted from the price. Find the discount amount, then subtract.

Example. A $120 jacket is marked "30% off." Discount = 0.30 x $120 = $36. Sale price = $120 - $36 = $84.

Shortcut: 30% off means you pay 70%, so $120 x 0.70 = $84. Whenever something is X% off, you pay (100 - X)% of the original.

Markups

A markup is a percent a business adds to its cost to set the selling price.

Example. A shop buys a part for $40 and marks it up 25%. Markup = 0.25 x $40 = $10. Selling price = $40 + $10 = $50. (Or in one step, $40 x 1.25 = $50.)

Percent Increase and Decrease

To describe how much a quantity changed as a percent, use:

Percent change = (change / original) x 100

Example (increase). Production rose from 400 units to 460 units. Change = 460 - 400 = 60. Percent increase = 60 / 400 = 0.15 = 15%.

Example (decrease). A workforce dropped from 250 to 230 workers. Change = 250 - 230 = 20. Percent decrease = 20 / 250 = 0.08 = 8%.

The key is to divide by the original (starting) value, not the new one.

Commissions

A commission is a percent of sales paid to a salesperson.

Example. A rep earns 6% commission and sells $14,500 this week. Commission = 0.06 x $14,500 = $870.

Some jobs pay a base salary plus commission.

Example. A salesperson earns $500 base plus 4% of sales. On $9,000 in sales: commission = 0.04 x $9,000 = $360. Total pay = $500 + $360 = $860.

Tips

A tip (gratuity) is a percent of a bill, common in service work.

Example. A catering bill is $240 and the customer adds an 18% tip. Tip = 0.18 x $240 = $43.20. Total charged = $240 + $43.20 = $283.20.

A quick mental shortcut for a 20% tip: find 10% by moving the decimal one place left ($240 becomes $24.00), then double it to get $48.00. Many tip questions can be estimated this way and then adjusted, which is faster than reaching for the calculator on every step.

Defect and Completion Rates

Quality-control questions describe how many items are good or bad as a percent.

Example (defect rate). A run of 1,500 parts has 45 defects. Defect rate = 45 / 1,500 = 0.03 = 3%.

Example (finding the count). If a 2% defect rate is expected on 5,000 parts, the number of defects = 0.02 x 5,000 = 100 parts.

Example (completion rate). A team finished 342 of 360 scheduled repairs. Completion rate = 342 / 360 = 0.95 = 95%.

Example (pass rate from a defect rate). If 3% of parts are defective, then 97% pass. Out of 1,500 parts, the good ones number 0.97 x 1,500 = 1,455 parts - the same as 1,500 - 45. Defect rate and pass rate always add to 100%, so you can find either one from the other.

Quick Reference

One Multi-Step Example

A salesperson earns 5% commission. This month they sold $22,000, but $2,000 of that was returned. First find net sales: $22,000 - $2,000 = $20,000. Commission = 0.05 x $20,000 = $1,000. Always adjust the base amount before applying the percent, and double-check whether the percent is being added (tax, tip, markup) or subtracted (discount) - the direction of the change is where most of the points on percentage questions are won or lost.