Ratio & Proportion MCQ & Objective Questions
Understanding Ratio & Proportion is crucial for students preparing for exams in India. This topic not only forms a significant part of the curriculum but also appears frequently in various competitive exams. Practicing MCQs and objective questions on Ratio & Proportion enhances your problem-solving skills and boosts your confidence, ensuring you score better in your assessments.
What You Will Practise Here
Fundamentals of Ratio and Proportion
Types of Ratios: Simple, Compound, and Inverse Ratios
Proportional Relationships and their Applications
Solving Problems Involving Direct and Inverse Proportions
Key Formulas and Definitions Related to Ratios
Word Problems and Real-Life Applications of Ratios
Diagrams and Visual Representations of Ratios
Exam Relevance
Ratio & Proportion is a vital topic in the CBSE syllabus and is also included in various State Boards. Students can expect questions based on this concept in competitive exams like NEET and JEE. Typically, questions may involve solving for unknowns, applying ratios in real-life scenarios, or interpreting data presented in different forms. Familiarity with common question patterns will help you tackle these problems efficiently.
Common Mistakes Students Make
Confusing ratios with fractions and not understanding their differences.
Overlooking the importance of units when solving proportion problems.
Misinterpreting word problems, leading to incorrect setups of equations.
Neglecting to simplify ratios before solving, which can lead to complex calculations.
FAQs
Question: What are the basic properties of ratios?Answer: Ratios compare two quantities and can be simplified like fractions. They maintain the same value when both terms are multiplied or divided by the same non-zero number.
Question: How can I improve my skills in Ratio & Proportion?Answer: Regular practice of Ratio & Proportion MCQ questions and understanding the underlying concepts will significantly enhance your skills and confidence.
Don't wait any longer! Dive into our practice MCQs on Ratio & Proportion to test your understanding and excel in your exams. Every question you solve brings you one step closer to mastering this essential topic!
Q. If 15 workers can build a wall in 30 days, how many days will it take for 5 workers to build the same wall?
A.
60 days
B.
75 days
C.
90 days
D.
100 days
Show solution
Solution
Total work = 15 workers * 30 days = 450 worker-days. For 5 workers, days = 450 / 5 = 90 days.
Correct Answer:
C
— 90 days
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Q. If 2 kg of sugar costs $5, how much will 5 kg of sugar cost?
A.
$10
B.
$12.5
C.
$15
D.
$20
Show solution
Solution
Cost per kg = $5 / 2 kg = $2.5. For 5 kg, cost = 5 * 2.5 = $12.5.
Correct Answer:
B
— $12.5
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Q. If 3 machines can produce 150 units in 5 hours, how many units can 6 machines produce in 5 hours?
A.
150 units
B.
300 units
C.
450 units
D.
600 units
Show solution
Solution
If 3 machines produce 150 units, then 6 machines will produce 150 * 2 = 300 units.
Correct Answer:
B
— 300 units
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Q. If 3 machines can produce 150 units in 5 hours, how many units can 6 machines produce in 2 hours?
A.
60 units
B.
90 units
C.
120 units
D.
150 units
Show solution
Solution
Rate of production = 150 units / 5 hours = 30 units/hour for 3 machines. For 6 machines, rate = 60 units/hour. In 2 hours, they produce 60 * 2 = 120 units.
Correct Answer:
C
— 120 units
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Q. If 3 machines can produce 150 units in 5 hours, how many units can 6 machines produce in 10 hours?
A.
300 units
B.
450 units
C.
600 units
D.
750 units
Show solution
Solution
3 machines produce 150 units in 5 hours, so 6 machines will produce 300 units in 5 hours. In 10 hours, they will produce 600 units.
Correct Answer:
C
— 600 units
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Q. If 4 bicycles can be repaired in 6 hours, how many bicycles can be repaired in 18 hours by 6 bicycles?
A.
12 bicycles
B.
15 bicycles
C.
18 bicycles
D.
24 bicycles
Show solution
Solution
Rate = 4 bicycles / 6 hours = 2/3 bicycles/hour. For 6 bicycles, rate = 4 bicycles/hour. In 18 hours, they can repair 4 * 18 = 72 bicycles.
Correct Answer:
D
— 24 bicycles
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Q. If 4 people can complete a project in 12 days, how many people are needed to complete the project in 6 days?
A.
6 people
B.
8 people
C.
10 people
D.
12 people
Show solution
Solution
If 4 people take 12 days, then to complete in 6 days, we need 4 * 12 / 6 = 8 people.
Correct Answer:
B
— 8 people
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Q. If 4 people can complete a task in 10 days, how many people are needed to complete the task in 5 days?
A.
6 people
B.
8 people
C.
10 people
D.
12 people
Show solution
Solution
Total work = 4 people * 10 days = 40 person-days. To complete in 5 days, needed people = 40 / 5 = 8 people.
Correct Answer:
B
— 8 people
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Q. If 6 people can finish a job in 8 days, how many people are needed to finish the job in 4 days?
A.
8 people
B.
10 people
C.
12 people
D.
14 people
Show solution
Solution
6 people take 8 days, so total work = 6 * 8 = 48 person-days. To finish in 4 days, needed people = 48 / 4 = 12 people.
Correct Answer:
C
— 12 people
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Q. If 6 workers can build a wall in 8 days, how many workers are needed to build the wall in 4 days?
A.
8 workers
B.
10 workers
C.
12 workers
D.
14 workers
Show solution
Solution
Work = 6 workers * 8 days = 48 worker-days. To finish in 4 days, needed = 48 worker-days / 4 days = 12 workers.
Correct Answer:
C
— 12 workers
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Q. If 6 workers can finish a job in 15 days, how many days will it take for 3 workers to finish the same job?
A.
30 days
B.
35 days
C.
40 days
D.
45 days
Show solution
Solution
Total work = 6 workers * 15 days = 90 worker-days. For 3 workers, days = 90 / 3 = 30 days.
Correct Answer:
C
— 40 days
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Q. If 7 workers can complete a job in 14 days, how many workers are needed to complete the job in 7 days?
A.
10 workers
B.
12 workers
C.
14 workers
D.
16 workers
Show solution
Solution
7 workers * 14 days = 98 worker-days. For 7 days, needed = 98 / 7 = 14 workers.
Correct Answer:
C
— 14 workers
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Q. If 8 liters of paint can cover 100 square meters, how many liters are needed to cover 250 square meters?
A.
15 liters
B.
16 liters
C.
20 liters
D.
25 liters
Show solution
Solution
8 liters cover 100 square meters, so for 250 square meters, (250/100) * 8 = 20 liters.
Correct Answer:
C
— 20 liters
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Q. If 8 people can complete a project in 12 days, how many people are needed to complete the project in 6 days?
A.
12 people
B.
16 people
C.
20 people
D.
24 people
Show solution
Solution
If 8 people take 12 days, then the total work is 8 * 12 = 96 person-days. To complete in 6 days, needed people = 96 / 6 = 16 people.
Correct Answer:
B
— 16 people
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Q. If 8 people can finish a project in 12 days, how many people are needed to finish the project in 6 days?
A.
12 people
B.
16 people
C.
20 people
D.
24 people
Show solution
Solution
Work done = People * Days. 8 * 12 = 96 person-days. To finish in 6 days, needed = 96 / 6 = 16 people.
Correct Answer:
B
— 16 people
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Q. If 8 workers can build a wall in 12 days, how many days will it take for 4 workers to build the same wall?
A.
24 days
B.
30 days
C.
36 days
D.
48 days
Show solution
Solution
If 8 workers take 12 days, then 4 workers will take 12 * (8/4) = 24 days.
Correct Answer:
C
— 36 days
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Q. If 8 workers can build a wall in 15 days, how many days will it take for 4 workers to build the same wall?
A.
30 days
B.
35 days
C.
40 days
D.
45 days
Show solution
Solution
8 workers take 15 days, so total work = 8 * 15 = 120 worker-days. For 4 workers, days = 120 / 4 = 30 days.
Correct Answer:
C
— 40 days
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Q. If 8 workers can complete a job in 12 days, how many days will it take for 4 workers to complete the same job?
A.
24 days
B.
30 days
C.
36 days
D.
48 days
Show solution
Solution
If 8 workers take 12 days, then 4 workers will take 12 * (8/4) = 24 days.
Correct Answer:
C
— 36 days
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Q. If the ratio of the lengths of two rectangles is 5:7 and the length of the first rectangle is 25 cm, what is the length of the second rectangle?
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Solution
Let the length of the first rectangle = 5x and the second = 7x. Given 5x = 25, x = 5. Therefore, length of the second rectangle = 7x = 7*5 = 35.
Correct Answer:
A
— 30
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Q. If the ratio of the lengths of two rectangles is 7:4 and the length of the first rectangle is 28 cm, what is the length of the second rectangle?
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Solution
Let the lengths be 7x and 4x. Given 7x = 28, x = 4. Therefore, the length of the second rectangle = 4x = 4*4 = 16.
Correct Answer:
A
— 16
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Q. If the ratio of the lengths of two ropes is 5:7 and the total length of the ropes is 72 meters, what is the length of the shorter rope?
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Solution
Let the lengths be 5x and 7x. Given 5x + 7x = 72, 12x = 72, x = 6. Therefore, shorter rope = 5x = 5*6 = 30.
Correct Answer:
B
— 25
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Q. If the ratio of the lengths of two sides of a triangle is 3:5 and the perimeter is 64 cm, what is the length of the longer side?
Show solution
Solution
Let the sides be 3x and 5x. Then, 3x + 5x = 64, 8x = 64, x = 8. Therefore, the longer side = 5x = 5*8 = 40.
Correct Answer:
B
— 25
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Q. If the ratio of the lengths of two sides of a triangle is 7:9 and the longer side is 36 cm, what is the length of the shorter side?
Show solution
Solution
Let the shorter side be 7x and the longer side be 9x. Given 9x = 36, x = 4. Therefore, shorter side = 7x = 7*4 = 28.
Correct Answer:
A
— 28
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Q. If the ratio of the number of apples to oranges is 7:3 and there are 42 apples, how many oranges are there?
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Solution
Let apples = 7x and oranges = 3x. Given 7x = 42, x = 6. Therefore, oranges = 3x = 3*6 = 18.
Correct Answer:
A
— 18
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Q. If the ratio of the speeds of two cars is 5:7 and the faster car travels 140 km in an hour, how far does the slower car travel in the same time?
A.
100
B.
120
C.
140
D.
160
Show solution
Solution
Let speeds be 5x and 7x. Given 7x = 140, x = 20. Slower car's speed = 5x = 5*20 = 100 km.
Correct Answer:
A
— 100
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Q. If the ratio of two numbers is 7:9 and their sum is 128, what are the two numbers?
A.
56, 72
B.
49, 81
C.
63, 72
D.
70, 58
Show solution
Solution
Let the numbers be 7x and 9x. Then, 7x + 9x = 128, 16x = 128, x = 8. Therefore, the numbers are 7*8 = 56 and 9*8 = 72.
Correct Answer:
A
— 56, 72
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Q. If the ratio of two numbers is 7:9 and their sum is 128, what is the larger number?
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Solution
Let the numbers be 7x and 9x. Then, 7x + 9x = 128, 16x = 128, x = 8. Larger number = 9x = 9*8 = 72.
Correct Answer:
A
— 72
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Q. In a class, the ratio of boys to girls is 2:3. If there are 15 girls, how many boys are there?
Show solution
Solution
Let boys be 2x and girls be 3x. Given 3x = 15, x = 5. Therefore, boys = 2x = 2*5 = 10.
Correct Answer:
A
— 10
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Q. In a class, the ratio of boys to girls is 5:3. If there are 40 students in total, how many girls are there?
Show solution
Solution
Let boys be 5x and girls be 3x. Then, 5x + 3x = 40, 8x = 40, x = 5. Therefore, girls = 3x = 3*5 = 15.
Correct Answer:
A
— 15
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Q. In a class, the ratio of students who passed to those who failed is 5:3. If 40 students passed, how many failed?
Show solution
Solution
Let passed = 5x and failed = 3x. Given 5x = 40, x = 8. Therefore, failed = 3x = 3*8 = 24.
Correct Answer:
A
— 24
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