Ratio Word Problems — Practice Set

Bank code: WRD-RAT · Section: Word Problems · 30 questions — Easy 5 · Medium 8 · Hard 12 · Extreme 5

Write every quantity as a multiple of k, then ask what stayed the same - the invariant is what turns a confusing story into a single equation.

Every question below is live in the question bank under the ID shown — the sheet and the portal are the same questions. Attempt a level with the clock running, then check Part C.

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Part A — Questions

Quantitative Comparison — the four choices are always the same, so they are not reprinted: (A) Column A is greater · (B) Column B is greater · (C) The two quantities are equal · (D) The relationship cannot be determined from the information given

Level 1 · Easy — 5 questions · ~4 min

warm-up — these must be automatic

Q1 · WRD-RAT-003 · Numeric Entry · 45s

$120 is divided between Alice and Bob in the ratio 3:5. How many dollars does Alice receive? Enter your answer as a number.

Numeric entry — write the number.

Q2 · WRD-RAT-006 · MCQ · 40s

A recipe calls for flour and sugar in the ratio 5:2. A baker uses 20 cups of flour. How many cups of sugar are needed?

(A) 4
(B) 8
(C) 10
(D) 28
(E) 50

Q3 · WRD-RAT-007 · Numeric Entry · 50s

In a class the ratio of students who passed a test to students who failed it is 7:3. If 21 students passed, how many students are in the class? Enter your answer as a number.

Numeric entry — write the number.

Q4 · WRD-RAT-009 · QC · 45s

A mixture consists only of water and juice, and the ratio of water to juice is 2:3.

Column A: The fraction of the mixture that is water Column B: 2/5

Q5 · WRD-RAT-010 · MCQ · 55s

6 workers can build a wall in 12 days. Working at the same rate, how many days would 9 workers take to build the same wall?

(A) 4
(B) 8
(C) 9
(D) 12
(E) 18

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Level 2 · Medium — 8 questions · ~10 min

two or three steps, one planted trap each

Q6 · WRD-RAT-019 · MCQ · 85s

The ratio of men to women in an office is 5:4. If 3 men leave and 3 women are hired, the ratio becomes 1:1. How many people worked in the office originally?

(A) 6
(B) 24
(C) 27
(D) 30
(E) 54

Q7 · WRD-RAT-021 · Select all that apply · 80s

$200 is divided among A, B and C in the ratio 2:3:5. Which of the following amounts are among the three shares? Select all that apply.

(A) $20
(B) $40
(C) $60
(D) $80
(E) $100

Q8 · WRD-RAT-022 · MCQ · 80s

8 machines working together produce 400 units in 5 hours. Working at the same rate, how many units can 12 machines produce in 3 hours?

(A) 240
(B) 300
(C) 360
(D) 480
(E) 600

Q9 · WRD-RAT-023 · Numeric Entry · 85s

A and B are positive numbers with A:B = 3:8. When A alone is increased by 9, the ratio A:B becomes 3:4. What is the value of B? Enter your answer as a number.

Numeric entry — write the number.

Q10 · WRD-RAT-028 · MCQ · 70s

A shade of paint is made by mixing red and white paint in the ratio 3:1 by volume. A painter has exactly 12 liters of red paint and an unlimited supply of white paint. What is the greatest number of liters of the shade he can mix?

(A) 4
(B) 12
(C) 16
(D) 36
(E) 48

Q11 · WRD-RAT-030 · MCQ · 75s

Three partners invest in a business in the ratio 5:3:2, and the total investment is $150,000. Profits are shared in the same ratio as the investments. If the total profit for a year is $60,000, how much of that profit does the partner who invested least receive?

(A) $6,000
(B) $12,000
(C) $18,000
(D) $20,000
(E) $30,000

Q12 · WRD-RAT-031 · Select all that apply · 80s

In a parking lot the ratio of cars to trucks is 5:8, and every vehicle in the lot is either a car or a truck. Which of the following could be the total number of vehicles in the lot? Select all that apply.

(A) 26
(B) 40
(C) 52
(D) 65
(E) 80

Q13 · WRD-RAT-033 · QC · 75s

Solution P consists only of salt and water, in which the ratio of salt to water is 1:9. Solution Q consists only of salt and water, in which the ratio of salt to water is 2:13.

Column A: The fraction of solution P that is salt Column B: The fraction of solution Q that is salt

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Level 3 · Hard — 12 questions · ~20 min

where 162+ is won or lost

Q14 · WRD-RAT-034 · MCQ · 105s

A box contains only red and blue balls, in the ratio 3:5. After 6 red balls are added and nothing else changes, the ratio of red to blue is 3:4. How many more red balls must then be added, with no other change, to make the ratio of red to blue 1:1?

(A) 5
(B) 8
(C) 10
(D) 16
(E) 40

Q15 · WRD-RAT-035 · QC · 100s

x is a positive integer.

Column A: (x + 2)/(x + 5) Column B: (x + 5)/(x + 9)

Q16 · WRD-RAT-036 · Numeric Entry · 105s

A tank holds a mixture of liquids A, B and C in the ratio 3:4:5. Then 8 liters of A are removed and 8 liters of C are added, after which the ratio of A to B to C is 1:4:7. What was the original total volume of the mixture, in liters? Enter your answer as a number.

Numeric entry — write the number.

Q17 · WRD-RAT-037 · MCQ · 100s

At a factory the ratio of managers to supervisors is 2:3, the ratio of supervisors to technicians is 4:5, and the ratio of technicians to laborers is 3:7. If there are 210 laborers, how many managers are there?

(A) 48
(B) 60
(C) 72
(D) 90
(E) 108

Q18 · WRD-RAT-038 · QC · 100s

A box contains red, green and yellow balls in the ratio 2:3:4. Then 9 green balls are added to the box and no other change is made.

Column A: The ratio of red balls to green balls after the addition Column B: The ratio of red balls to yellow balls before the addition

Q19 · WRD-RAT-039 · Select all that apply · 95s

In a club the ratio of men to women is 5:3. Then a positive number of women join the club, and no one else joins or leaves. Which of the following MUST be true? Select all that apply.

(A) The number of men in the club did not change
(B) The ratio of men to women is now less than 5:3
(C) There are now more women in the club than men
(D) Men now make up a smaller fraction of the club than before
(E) The number of women in the club more than doubled

Q20 · WRD-RAT-041 · MCQ · 95s

In a school the ratio of teachers to students is 1:18, and among the students the ratio of male to female is 5:4. Every person in the school is either a teacher or a student. What fraction of the total school population is female students?

(A) 1/19
(B) 4/9
(C) 8/19
(D) 8/27
(E) 10/19

Q21 · WRD-RAT-042 · QC · 90s

P, Q and R are positive numbers with P:Q = 3:4 and Q:R = 5:6.

Column A: P/R Column B: 5/8

Q22 · WRD-RAT-044 · Numeric Entry · 105s

A sum of money is divided among A, B and C. A's share is to B's share as 3 is to 4, and B's share is to C's share as 6 is to 5. If B receives $180 more than C, what is the total sum of money, in dollars? Enter your answer as a number.

Numeric entry — write the number.

Q23 · WRD-RAT-045 · Select all that apply · 100s

A jar contains 3n red marbles and 5n blue marbles, where n is an integer greater than 1. Which of the following changes would make the ratio of red marbles to blue marbles strictly greater than 3:5? Select all that apply.

(A) Add 3 red marbles and 5 blue marbles
(B) Add 6 red marbles and no blue marbles
(C) Remove 3 red marbles and 3 blue marbles
(D) Double the number of marbles of each color
(E) Add 1 red marble and remove 1 blue marble

Q24 · WRD-RAT-051 · Numeric Entry · 110s

The monthly incomes of Ravi and Sunil are in the ratio 5:4, and their monthly expenditures are in the ratio 7:5. Each of them saves $900 per month, where savings equal income minus expenditure. What is Sunil's monthly expenditure, in dollars? Enter your answer as a number.

Numeric entry — write the number.

Q25 · WRD-RAT-052 · MCQ · 110s

A cash drawer contains only $1 bills, $5 bills and $10 bills, and the numbers of bills of the three kinds are in the ratio 4:3:2. The total value of the bills is $1,170. Some of the $5 bills are then exchanged for $10 bills of the same total value, after which the drawer contains equal numbers of $5 bills and $10 bills. How many $10 bills does the drawer then contain?

(A) 60
(B) 70
(C) 75
(D) 90
(E) 130

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Level 4 · Extreme — 5 questions · ~10 min

165+ — expect to need the insight, not the grind

Q26 · WRD-RAT-046 · MCQ · 120s

Working alone, tap A fills an empty tank in 6 hours, tap B fills it in 8 hours and tap C fills it in 12 hours. All three taps are opened at the same time into the empty tank, tap C is closed after a while, and the tank is exactly full 3 hours after the taps were opened. Taps A and B ran the whole time. For how many hours was tap C open?

(A) 0.5
(B) 1
(C) 1.5
(D) 2
(E) 3

Q27 · WRD-RAT-047 · Numeric Entry · 125s

The present ages of A, B, C and D are in the ratio 1:2:3:4. Five years from now their ages will be in the ratio 2:3:4:5. How many years from now will their ages be in the ratio 3:4:5:6? Enter your answer as a number.

Numeric entry — write the number.

Q28 · WRD-RAT-048 · MCQ · 130s

Liquids X and Y are combined in the ratio 3:2 by volume. The resulting mixture is then combined with liquid Z in the ratio 4:1 by volume, mixture to Z. Finally, 60 liters of liquid Y are added to that blend. If liquid Z now makes up exactly 1/6 of the blend by volume, how many liters of liquid X does the blend contain?

(A) 60
(B) 96
(C) 144
(D) 156
(E) 180

Q29 · WRD-RAT-049 · QC · 125s

In Company A the ratio of managers to workers is 1:9. In Company B the ratio of managers to workers is 1:11. Every employee of each company is either a manager or a worker. The two companies merge into a single company, and no one joins or leaves.

Column A: (number of managers)/(number of workers) in the merged company Column B: 1/10

Q30 · WRD-RAT-050 · Select all that apply · 125s

The positive quantities a, b, c and d satisfy a:b = 3:4, b:c = 6:5 and c:d = 2:3. Which of the following must be true? Select all that apply.

(A) a:d = 3:5
(B) a = d
(C) a:c = 3:5
(D) b is greater than c
(E) d is the greatest of the four quantities

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