ACT Math Practice Test: Ratios, Rates and Percent Word Problems
- Ratios, Rates and Percent Word Problems
- 10 questions
- 12 minutes
These 10 word problems practice the ratio, rate and percent skills that the ACT tests in everyday situations. Write down what each number stands for and its unit before you set up an equation; most wrong answers come from comparing the wrong two quantities.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
A car travels 210 miles on 7.5 gallons of gasoline. At the same rate, how many miles can it travel on 12 gallons?
Correct answer: C
The car gets 210 ÷ 7.5 = 28 miles per gallon, so 12 gallons take it 28 × 12 = 336 miles.
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Question 2
The price of a jacket is increased by 20%. Later, the new price is decreased by 20%. Compared with the original price, the final price is:
Correct answer: A
Multiply by 1.20 and then by 0.80: 1.20 × 0.80 = 0.96, so the final price is 96% of the original, 4% lower. The 20% decrease is taken from a larger amount than the 20% increase, so they do not cancel.
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Question 3
In a class of 36 students, the ratio of boys to girls is 4 : 5. How many girls are in the class?
Correct answer: D
The ratio has 4 + 5 = 9 parts, so each part is 36 ÷ 9 = 4 students. Girls are 5 parts: 5 × 4 = 20. The choice 16 is the number of boys.
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Question 4
Pipe A alone can fill a tank in 6 hours. Pipe B alone can fill the same tank in 3 hours. If both pipes are open, how many hours will it take to fill the empty tank?
Correct answer: B
Pipe A fills 1/6 of the tank per hour and pipe B fills 1/3, so together they fill 1/6 + 1/3 = 1/2 per hour and need 2 hours. The choice 4.5 averages the two times, but two pipes together must be faster than either one alone.
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Question 5
How many liters of a 40% acid solution must be added to 12 liters of a 15% acid solution to make a 25% acid solution?
Correct answer: A
Acid before mixing: 0.15(12) + 0.40x. Acid after: 0.25(12 + x). So 1.8 + 0.40x = 3 + 0.25x, 0.15x = 1.2 and x = 8. Check: 1.8 + 3.2 = 5 liters of acid in 20 liters is 25%.
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Question 6
A cyclist rides at 45 miles per hour down a long hill. What is this speed in feet per second? (1 mile = 5,280 feet)
Correct answer: C
Multiply by 5,280 to change miles to feet and divide by 3,600 to change hours to seconds: 45 × 5,280 ÷ 3,600 = 66 feet per second.
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Question 7
Lena deposits $2,400 in an account that earns 3.5% simple interest per year. She makes no other deposits or withdrawals. How much interest, in dollars, does the account earn in 4 years?
Correct answer: B
Simple interest is principal × rate × time: 2,400 × 0.035 × 4 = $336. The choice $84 is one year of interest, and $2,736 is the balance, not the interest.
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Question 8
The number 18 is 24% of what number?
Correct answer: D
Solve 0.24n = 18: n = 18 ÷ 0.24 = 75. The choice 4.32 is 24% of 18, the reverse question.
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Question 9
Two cyclists start 66 miles apart and ride toward each other on the same road. One rides at 12 miles per hour and the other at 10 miles per hour. After how many hours will they meet?
Correct answer: A
The distance between them shrinks by 12 + 10 = 22 miles each hour, so they meet after 66 ÷ 22 = 3 hours. The choice 5.5 is how long the faster cyclist would need to cover all 66 miles alone.
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Question 10
The population of a town grew from 12,500 to 14,000. By what percent did the population increase?
Correct answer: C
The increase is 1,500. Percent increase compares it with the original value: 1,500 ÷ 12,500 = 0.12 = 12%. Dividing by the new value, 14,000, gives about 10.7%, the common trap.
Questions you leave blank are not counted as wrong.
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