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Math Word Problems quiz

Percentage Word Problems Quiz

Practice 10 percentage word problems involving percent of a quantity, increase and decrease, reverse percentages, repeated changes, discounts, tax, markups, percentage points, and multi-step percent reasoning. Use hints when needed and review the explanation after each answer.

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1 Question 1 of 10
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A school club has 240 members. If 35% of the members volunteer at an event, how many members volunteer?

Hint: Convert 35% to 0.35 and multiply by the total number of members.
Explanation: 35% of 240 is 0.35 × 240 = 84. Therefore, 84 members volunteer.
2 Question 2 of 10
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A laptop originally costs $800. Its price is increased by 12%. What is the new price?

Hint: A 12% increase means the new price is 112% of the original price.
Explanation: 12% of $800 is $96. Add the increase: $800 + $96 = $896. Equivalently, $800 × 1.12 = $896.
3 Question 3 of 10
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A jacket is marked down from $150 to $114. What is the percent decrease?

Hint: Find the decrease first, then divide the decrease by the original price.
Explanation: The decrease is $150 - $114 = $36. Divide by the original price: 36 ÷ 150 = 0.24 = 24%.
4 Question 4 of 10
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After a 25% discount, a bicycle costs $360. What was the original price?

Hint: After a 25% discount, the sale price is 75% of the original price.
Explanation: Let the original price be x. Then 0.75x = 360, so x = 360 ÷ 0.75 = 480. The original price was $480.
5 Question 5 of 10
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A store reduces a $250 item by 20%, then increases the reduced price by 20%. What is the final price?

Hint: Apply each percentage to the current price, not to the original price both times.
Explanation: First decrease: $250 × 0.80 = $200. Then increase: $200 × 1.20 = $240. A 20% decrease followed by a 20% increase does not return to the original price.
6 Question 6 of 10
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A $120 pair of shoes is discounted by 30%, then 8% sales tax is applied to the discounted price. What is the final price?

Hint: Apply the discount first, then calculate tax on the discounted price.
Explanation: Discounted price: $120 × 0.70 = $84. Tax: $84 × 0.08 = $6.72. Final price = $84 + $6.72 = $90.72.
7 Question 7 of 10
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A shop buys a desk for $320 and marks it up by 35% of its cost. What selling price should the shop set?

Hint: A 35% markup means the selling price is 135% of the cost.
Explanation: Markup = 0.35 × $320 = $112. Selling price = $320 + $112 = $432. Equivalently, $320 × 1.35 = $432.
8 Question 8 of 10
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A town's population grows from 48,000 to 54,600. What is the percent increase?

Hint: Find the increase and divide it by the original population.
Explanation: The increase is 54,600 - 48,000 = 6,600. Then 6,600 ÷ 48,000 = 0.1375 = 13.75%.
9 Question 9 of 10
Not answered

A candidate's support rises from 42% to 49% in a poll. By how many percentage points did support increase, and what was the relative percent increase?

Hint: Percentage-point change is subtraction. Relative percent increase divides that change by the original 42%.
Explanation: The percentage-point increase is 49% - 42% = 7 points. Relative increase = 7 ÷ 42 ≈ 0.1667 = 16.7%.
10 Question 10 of 10
Not answered

A quantity is increased by 10% each year for two years. If it starts at 500, what is its value after two years?

Hint: Repeated percent growth compounds: multiply by 1.10 once for each year.
Explanation: After one year: 500 × 1.10 = 550. After two years: 550 × 1.10 = 605. Equivalently, 500 × 1.10² = 605.

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Percent reasoning lab

Percent problems are multiplier problems hidden inside everyday language

These 10 questions cover percent of a quantity, increase and decrease, reverse percentages, repeated changes, discounts, tax, markups, population growth, percentage points, and compound growth. The key is deciding which value is the base before doing any arithmetic.

Percent of a quantityIncreaseDecreaseReverse percent Discount + taxMarkupRepeated changePercentage points
Percent-change timeline

For percent increase or decrease, separate the amount of change from the rate of change

A price falls from $150 to $114. The dollar decrease is not the same thing as the percent decrease.

150Originalreference value
36Decrease150 − 114
0.24Rate36 ÷ 150
24%Percent decreasefinal result
Reverse-percent decoder

When the final price is known, divide by the remaining percentage

A 25% discount leaves 75% of the original price.

Sale price$360

Recover the original amount

75% of original = $360
0.75x = 360
x = 360 ÷ 0.75
original price = $480
Discount + tax receipt

Successive percentages apply to the current amount, not always to the original amount

For $120 shoes discounted 30%, the 8% tax is calculated on the discounted $84 price.

Original price$120.00
30% discount−$36.00
Discounted subtotal$84.00
8% tax+$6.72
Final price$90.72
Repeated changes

−20% and +20% do not cancel

$250 × 0.80 × 1.20 = $240
The second 20% is calculated from $200, not from the original $250. The bases are different.
Compound growth

Repeated growth multiplies repeatedly

500 × 1.10² = 605
Two years of 10% growth gives 21% total growth, not 20%, because year two grows from 550.
Markup ladder

Markup is measured from cost, so the cost is the percent base

A desk costs the shop $320 and is marked up by 35%.

Cost$320
35% markup$112
Selling price$432
Percent vs percentage points

A change from 42% to 49% has two valid descriptions — but they mean different things

Percentage-point change

Subtract the two percentages directly.

49% − 42% = 7 percentage points

Relative percent increase

Compare the 7-point increase with the original 42% base.

7 ÷ 42 ≈ 16.7%
After the quiz

Diagnose the type of percent reasoning that caused the error

The same arithmetic can produce a wrong answer if the percent base or multiplier is chosen incorrectly.

Direct percentfind p% of a known total
Changeincrease, decrease, markup
Reverse percentrecover the original amount
Repeated changesdiscount + tax, compounding, successive multipliers
Math Word Problems Rates & Proportions