Percentage Word Problems (with Answers)

How to solve percentage word problems

Quick answer: find the whole, which is the amount the percentage is of, turn the percentage into a decimal, then use part = rate × whole. For the $80 jacket at 30% off, 30% of 80 is 24, so you pay $80 − $24 = $56.

The three-step method

1. 1Find the whole. It is the number after "of", or the original or starting amount.
2. 2Turn the percentage into a decimal by dividing by 100, so 8.5% is 0.085.
3. 3Decide which piece is missing, the part, the rate or the whole, and solve for it. Then put your answer back into the problem to check it.

Here the rate is the decimal form of the percentage. Multiply it by 100 to read the rate as a percent again.

Reading the wording

"Of" means multiply, so 40% of 30 is 0.4 × 30. "Is" means equals. "Off" and "discount" mean subtract the part from the whole, while "plus tax", "increase" and "tip" mean add it. "What percent" makes the rate the unknown, and "of what" makes the whole the unknown.

Percent problems without a calculator

Find 10% by moving the decimal point one place, then build from there. 15% of 240 is 10% (24) plus half of that (12), which is 36. For 1%, move the point two places.

Percentage change problems

When a value changes, the new amount is the old amount × (1 + rate), with a negative rate for a decrease. To find the rate, divide the change by the old value. To go backwards and find the old value, divide the new one by 1 + rate. This is where most hard problems go wrong, so problems 9 to 12 cover it.

Percentage word problems with answers

The problems run from easy to hard. Work each one before you read the solution.

Percentage worksheet with answer key

Ten percentage questions with no worked solutions, as percentage practice problems in the same order of difficulty. Cover the key and try them first. Most percentage worksheets give the answer without the working, so use the 12 worked problems above to check your method.

1. 1What is 15% of 240?
2. 2What percent of 80 is 20?
3. 312 is 30% of what number?
4. 4A $65 pair of shoes is 20% off. What is the sale price?
5. 5A $120 bill has a 15% tip added. What is the total?
6. 6A phone rises in price from $400 to $460. What is the percent increase?
7. 7A share falls from $50 to $42. What is the percent decrease?
8. 8After a 25% increase a bike costs $250. What did it cost before?
9. 9A $90 item is 10% off, then a further 10% off. What is the final price?
10. 10A recipe uses 2.5 cups of flour and is scaled up by 40%. How much flour does it need?

Percentage worksheet with answer key

Percentage word problem code

These functions take rates as percentages, such as 8.5 for 8.5%, and return the numbers used in the problems above. The JavaScript version works in floating point, so round the result when you display it. The Python version uses exact fractions, so 8.5% of 60 is exactly 51/10.

JavaScript

1export function percentOf(rate, whole) {2  return (whole * rate) / 100;3}4​5export function whatPercent(part, whole) {6  if (whole === 0) throw new RangeError("whole must not be zero");7  return (part / whole) * 100;8}9​10export function wholeFrom(part, rate) {11  if (rate === 0) throw new RangeError("rate must not be zero");12  return (part * 100) / rate;13}14​15export function applyChange(value, rate) {16  return (value * (100 + rate)) / 100;17}18​19export function undoChange(value, rate) {20  if (rate === -100) throw new RangeError("a 100% decrease cannot be undone");21  return (value * 100) / (100 + rate);22}23​24export function percentChange(oldValue, newValue) {25  if (oldValue === 0) throw new RangeError("old value must not be zero");26  return ((newValue - oldValue) / Math.abs(oldValue)) * 100;27}

Python

1from fractions import Fraction2​3​4def _f(x):5    return Fraction(str(x))6​7​8def percent_of(rate, whole):9    return _f(whole) * _f(rate) / 10010​11​12def what_percent(part, whole):13    if _f(whole) == 0:14        raise ZeroDivisionError("whole must not be zero")15    return _f(part) / _f(whole) * 10016​17​18def whole_from(part, rate):19    if _f(rate) == 0:20        raise ZeroDivisionError("rate must not be zero")21    return _f(part) * 100 / _f(rate)22​23​24def apply_change(value, rate):25    return _f(value) * (100 + _f(rate)) / 10026​27​28def undo_change(value, rate):29    if _f(rate) == -100:30        raise ZeroDivisionError("a 100% decrease cannot be undone")31    return _f(value) * 100 / (100 + _f(rate))32​33​34def percent_change(old, new):35    if _f(old) == 0:36        raise ZeroDivisionError("old value must not be zero")37    return (_f(new) - _f(old)) / abs(_f(old)) * 100

For Problem 11, applyChange(applyChange(200, -25), 8) returns 162. For Problem 12, undoChange(48300, 15) returns 42000. percentChange divides by the absolute old value, so a loss shrinking from −50 to −25 reads +50%, the same convention as the percentage change calculator.

Privacy and input safety

The practice set runs in your browser. Answers are part of the page text, nothing you type is sent to a server or stored, and the page is a practice aid, not a timed test.

If a check-your-answer box is added, it accepts a number with an optional $ or % sign and optional thousands separators, applies the same comma rule as the other calculators (a comma followed by exactly three digits is a thousands separator, any other comma is a decimal point), and accepts an answer within half a unit of the last decimal place shown. Text, empty fields, NaN and Infinity are rejected with a message, and nothing typed is ever evaluated as code.

Common percentage problem mistakes

Percentage word problems by type

Most percent word problems are one of the first three types with an extra step. Spot the type, name the whole, then solve.