Quantitative Aptitude (SSC)

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Q. The average of two numbers is 30. If one number is 10 more than the other, what are the two numbers?

A. 20, 40
B. 25, 35
C. 30, 30
D. 15, 45

Solution

Let the numbers be x and x+10. (x + (x + 10)) / 2 = 30. Solving gives x = 25, so numbers are 25 and 35.

Correct Answer: B — 25, 35

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Q. The average of two numbers is 36. If one number is 40, what is the other number?

A. 32
B. 34
C. 36
D. 38

Solution

Let the other number be x. (40 + x) / 2 = 36. Solving gives x = 32.

Correct Answer: A — 32

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Q. The average score of 5 students is 80. If one more student joins and the new average becomes 82, what is the score of the new student?

A. 84
B. 86
C. 88
D. 90

Solution

Total score of 5 students = 5 * 80 = 400. New total score for 6 students = 6 * 82 = 492. Score of new student = 492 - 400 = 92.

Correct Answer: B — 86

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Q. The equation x^2 - 9 = 0 has roots that are: (2019)

A. -3 and 3
B. 0 and 9
C. 3 and 9
D. 1 and -1

Solution

Factoring gives (x-3)(x+3)=0, hence the roots are -3 and 3.

Correct Answer: A — -3 and 3

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Q. The LCM of two numbers is 84 and their HCF is 12. What is the sum of the two numbers if they are in the ratio 2:7?

A. 42
B. 56
C. 70
D. 84

Solution

Let the numbers be 2x and 7x. Then, HCF(2x, 7x) = x = 12, so x = 12. The numbers are 24 and 84. Their sum is 108.

Correct Answer: C — 70

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Q. The ratio of the lengths of two ropes is 1:4. If the longer rope is 32 meters long, how long is the shorter rope?

A. 8
B. 10
C. 12
D. 6

Solution

Let the lengths be x and 4x. Given 4x = 32, x = 8. Therefore, shorter rope = 8 meters.

Correct Answer: A — 8

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Q. The ratio of the lengths of two sides of a triangle is 3:4. If the longer side is 32 cm, what is the length of the shorter side?

A. 24
B. 20
C. 30
D. 28

Solution

Let the shorter side be 3x and the longer side be 4x. Given 4x = 32, x = 8. Therefore, the shorter side = 3x = 3*8 = 24.

Correct Answer: A — 24

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Q. The ratio of the lengths of two sides of a triangle is 3:4. If the perimeter of the triangle is 70 cm, what is the length of the longer side?

A. 30
B. 28
C. 32
D. 35

Solution

Let the sides be 3x and 4x. Then, 3x + 4x + base = 70. Assuming base = 0, 7x = 70, x = 10. Longer side = 4x = 40.

Correct Answer: A — 30

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Q. The ratio of the number of apples to oranges in a basket is 2:3. If there are 30 oranges, how many apples are there?

A. 20
B. 25
C. 15
D. 10

Solution

Let apples = 2x and oranges = 3x. Given 3x = 30, x = 10. Therefore, apples = 2x = 2*10 = 20.

Correct Answer: A — 20

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Q. The ratio of the number of apples to oranges in a basket is 5:3. If there are 40 apples, how many oranges are there?

A. 24
B. 30
C. 20
D. 32

Solution

Let apples = 5x and oranges = 3x. Given 5x = 40, x = 8. Therefore, oranges = 3x = 3*8 = 24.

Correct Answer: A — 24

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Q. The ratio of the number of students in two classes is 2:3. If there are 60 students in total, how many students are in the larger class?

A. 36
B. 30
C. 24
D. 20

Solution

Let students in class 1 = 2x and class 2 = 3x. Then, 2x + 3x = 60, 5x = 60, x = 12. Larger class = 3x = 3*12 = 36.

Correct Answer: A — 36

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Q. The ratio of the speeds of two cars is 2:3. If the faster car travels 180 km in 2 hours, how far does the slower car travel in the same time?

A. 120
B. 90
C. 150
D. 100

Solution

Speed of faster car = 180/2 = 90 km/h. Speed of slower car = (2/3)*90 = 60 km/h. Distance = speed * time = 60*2 = 120 km.

Correct Answer: A — 120

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Q. The ratio of the speeds of two cars is 3:4. If the faster car travels 120 km in 2 hours, how far does the slower car travel in the same time?

A. 80
B. 90
C. 100
D. 70

Solution

Let the speeds be 3x and 4x. Given 4x = 60 km/h, x = 15. Therefore, slower car's speed = 3x = 3*15 = 45 km/h. Distance = speed * time = 45 * 2 = 90 km.

Correct Answer: A — 80

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Q. The ratio of the speeds of two cars is 3:4. If the first car travels 120 km in 2 hours, how far does the second car travel in the same time?

A. 160
B. 180
C. 200
D. 150

Solution

Speed of first car = 120 km / 2 hours = 60 km/h. Let speed of second car = 4x. 3x = 60, x = 20. Therefore, speed of second car = 4*20 = 80 km/h. Distance = speed * time = 80 * 2 = 160 km.

Correct Answer: A — 160

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Q. The ratio of the speeds of two cars is 3:4. If the first car travels 120 km, how far does the second car travel?

A. 160
B. 150
C. 180
D. 140

Solution

Let the speed of the first car be 3x and the second car be 4x. The distance traveled is proportional to speed. Therefore, if 3x = 120, then 4x = (4/3)*120 = 160.

Correct Answer: A — 160

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Q. The roots of the equation x^2 + 6x + 8 = 0 are:

A. -2 and -4
B. -1 and -8
C. 2 and 4
D. 1 and -8

Solution

Factoring gives (x+2)(x+4)=0, hence the roots are -2 and -4.

Correct Answer: A — -2 and -4

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Q. The roots of the equation x^2 + 6x + 9 = 0 are:

A. -3 and -3
B. 3 and 3
C. 0 and 9
D. 1 and 8

Solution

The equation can be factored as (x+3)(x+3)=0, giving the double root x=-3.

Correct Answer: A — -3 and -3

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Q. The roots of the equation x^2 - 7x + 10 = 0 are: (2019)

A. 1 and 10
B. 2 and 5
C. 3 and 4
D. 5 and 2

Solution

Factoring gives (x-2)(x-5)=0, hence the roots are 2 and 5.

Correct Answer: C — 3 and 4

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Q. The volume of a cube is 125 cm³. What is the length of one side?

A. 5 cm
B. 10 cm
C. 15 cm
D. 20 cm

Solution

Volume = side³, so side = ∛125 cm³ = 5 cm.

Correct Answer: A — 5 cm

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Q. Two cars start from the same point and drive in opposite directions. Car A travels at 70 km/h and Car B at 90 km/h. How far apart will they be after 1 hour?

A. 160 km
B. 150 km
C. 140 km
D. 130 km

Solution

Distance apart = (Speed of A + Speed of B) × Time = (70 km/h + 90 km/h) × 1 h = 160 km.

Correct Answer: A — 160 km

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Q. Two cars start from the same point and travel in opposite directions. Car A travels at 70 km/h and Car B at 90 km/h. How far apart will they be after 1 hour?

A. 160 km
B. 150 km
C. 140 km
D. 130 km

Solution

Distance apart = (Speed of A + Speed of B) × Time = (70 km/h + 90 km/h) × 1 h = 160 km.

Correct Answer: A — 160 km

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Q. Two cars start from the same point and travel in opposite directions. Car A travels at 70 km/h and Car B at 50 km/h. How far apart will they be after 2 hours?

A. 240 km
B. 220 km
C. 200 km
D. 180 km

Solution

Distance = (70 km/h + 50 km/h) × 2 h = 240 km.

Correct Answer: A — 240 km

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Q. Two cars start from the same point and travel in opposite directions. Car A travels at 70 km/h and Car B at 90 km/h. How far apart will they be after 2 hours?

A. 320 km
B. 340 km
C. 360 km
D. 380 km

Solution

Relative speed = 70 km/h + 90 km/h = 160 km/h. Distance apart after 2 hours = 160 km/h × 2 h = 320 km.

Correct Answer: C — 360 km

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Q. Two cyclists start from the same point and ride in opposite directions. Cyclist A rides at 12 km/h and Cyclist B at 16 km/h. How far apart will they be after 1.5 hours?

A. 42 km
B. 48 km
C. 54 km
D. 60 km

Solution

Distance apart = (Speed of A + Speed of B) × Time = (12 km/h + 16 km/h) × 1.5 h = 42 km.

Correct Answer: B — 48 km

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Q. Two cyclists start from the same point and ride in the same direction. Cyclist A rides at 12 km/h and Cyclist B at 15 km/h. How long will it take for Cyclist B to be 9 km ahead of Cyclist A?

A. 3 hours
B. 4 hours
C. 5 hours
D. 6 hours

Solution

Relative speed = 15 km/h - 12 km/h = 3 km/h. Time = Distance / Speed = 9 km / 3 km/h = 3 hours.

Correct Answer: A — 3 hours

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Q. Two cyclists start from the same point and ride in the same direction. Cyclist A rides at 12 km/h and Cyclist B at 15 km/h. How far apart will they be after 2 hours?

A. 3 km
B. 4 km
C. 5 km
D. 6 km

Solution

Relative speed = 15 km/h - 12 km/h = 3 km/h. Distance apart = Relative speed × Time = 3 km/h × 2 h = 6 km.

Correct Answer: B — 4 km

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Q. Two cyclists start from the same point and ride in the same direction. Cyclist A rides at 10 km/h and Cyclist B at 15 km/h. How far apart will they be after 2 hours?

A. 5 km
B. 10 km
C. 15 km
D. 20 km

Solution

Relative speed = 15 km/h - 10 km/h = 5 km/h. Distance apart = Relative speed × Time = 5 km/h × 2 h = 10 km.

Correct Answer: B — 10 km

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Q. Two liquids A and B are mixed in the ratio 2:3. If the total volume of the mixture is 50 liters, how much liquid A is there?

A. 20 liters
B. 30 liters
C. 25 liters
D. 15 liters

Solution

Total parts = 2 + 3 = 5. Liquid A = (2/5) * 50 = 20 liters.

Correct Answer: A — 20 liters

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Q. Two liquids A and B are mixed in the ratio 3:2. If the total volume of the mixture is 50 liters, how much of liquid A is there?

A. 20 liters
B. 25 liters
C. 30 liters
D. 35 liters

Solution

Total parts = 3 + 2 = 5. Volume of A = (3/5) * 50 = 30L.

Correct Answer: C — 30 liters

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Q. Two liquids A and B are mixed in the ratio 4:1. If there are 25 liters of the mixture, how much liquid A is present?

A. 20 liters
B. 15 liters
C. 10 liters
D. 5 liters

Solution

In a 4:1 ratio, the total parts = 4 + 1 = 5. Liquid A = (4/5) * 25 = 20 liters.

Correct Answer: A — 20 liters

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Quantitative Aptitude (SSC) MCQ & Objective Questions

Quantitative Aptitude is a crucial component of various exams, especially for students preparing for the SSC (Staff Selection Commission) exams. Mastering this subject not only enhances problem-solving skills but also boosts confidence in tackling objective questions. Regular practice with MCQs and practice questions is essential for scoring better and understanding important concepts effectively.

What You Will Practise Here

Number Systems and their properties
Percentage, Ratio, and Proportion calculations
Time, Speed, and Distance problems
Simple and Compound Interest concepts
Algebraic expressions and equations
Data Interpretation and analysis
Mensuration and Geometry basics

Exam Relevance

Quantitative Aptitude is a significant part of the syllabus for CBSE, State Boards, and competitive exams like NEET and JEE. In these exams, students can expect questions that assess their ability to apply mathematical concepts to real-world scenarios. Common question patterns include direct problem-solving, data interpretation, and application of formulas, making it essential for students to be well-prepared.

Common Mistakes Students Make

Misunderstanding the problem statement leading to incorrect assumptions
Neglecting to apply the correct formulas in calculations
Overlooking units of measurement in word problems
Rushing through questions without double-checking calculations

FAQs

Question: What are the best ways to prepare for Quantitative Aptitude in SSC exams?
Answer: Regular practice with MCQs, understanding key concepts, and solving previous years' question papers are effective strategies.

Question: How can I improve my speed in solving Quantitative Aptitude questions?
Answer: Practicing timed quizzes and focusing on shortcut methods can significantly enhance your speed and accuracy.

Start your journey towards mastering Quantitative Aptitude today! Solve practice MCQs and test your understanding to achieve your exam goals. Remember, consistent practice is the key to success!

Quantitative Aptitude (SSC)

Quantitative Aptitude (SSC) MCQ & Objective Questions

What You Will Practise Here

Exam Relevance

Common Mistakes Students Make

FAQs

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