Direct & Inverse Proportion for Competitive Exam Success

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Direct & Inverse Proportion

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Direct & Inverse Proportion MCQ & Objective Questions

Understanding Direct & Inverse Proportion is crucial for students preparing for exams. This topic not only forms a fundamental part of mathematics but also appears frequently in objective questions. Practicing MCQs related to Direct & Inverse Proportion helps students enhance their problem-solving skills and boosts their confidence, ensuring better scores in exams.

What You Will Practise Here

Definitions and key concepts of Direct and Inverse Proportion
Formulas used in solving Direct & Inverse Proportion problems
Real-life applications of Direct & Inverse Proportion
Graphical representation and interpretation of proportional relationships
Worked examples and step-by-step solutions
Practice questions with varying difficulty levels
Important Direct & Inverse Proportion MCQ questions for exams

Exam Relevance

Direct & Inverse Proportion is a significant topic in various examinations, including CBSE, State Boards, NEET, and JEE. Students can expect questions that test their understanding of the concepts, application of formulas, and problem-solving abilities. Common question patterns include finding missing values in proportional relationships and interpreting word problems that involve direct or inverse variations.

Common Mistakes Students Make

Confusing Direct Proportion with Inverse Proportion
Misapplying formulas due to lack of understanding of the concepts
Overlooking units of measurement in word problems
Failing to interpret graphs correctly
Rushing through calculations, leading to simple arithmetic errors

FAQs

Question: What is the difference between Direct and Inverse Proportion?
Answer: Direct Proportion means that as one quantity increases, the other also increases, while Inverse Proportion means that as one quantity increases, the other decreases.

Question: How can I identify if a problem involves Direct or Inverse Proportion?
Answer: Look for keywords in the problem; if it mentions "together" or "for every," it is likely Direct Proportion, while "per" or "for each" often indicates Inverse Proportion.

Start your journey towards mastering Direct & Inverse Proportion by solving practice MCQs today! Testing your understanding through objective questions will not only prepare you for exams but also solidify your grasp of these essential concepts.

Q. A car travels 120 km in 2 hours. How long will it take to travel 180 km at the same speed?

A. 2.5 hours
B. 3 hours
C. 3.5 hours
D. 4 hours

Solution

Speed = 120 km / 2 hours = 60 km/h. Time = Distance / Speed = 180 km / 60 km/h = 3 hours.

Correct Answer: B — 3 hours

Q. A car travels 120 km in 2 hours. How long will it take to travel 300 km at the same speed?

A. 4 hours
B. 5 hours
C. 6 hours
D. 7 hours

Solution

Speed = 120 km / 2 hours = 60 km/h. Time = Distance / Speed = 300 km / 60 km/h = 5 hours.

Correct Answer: B — 5 hours

Q. A car uses 10 liters of fuel to travel 100 km. How much fuel will it need to travel 250 km?

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

Solution

Fuel consumption is 10 liters for 100 km, so for 250 km, it will need (250/100) * 10 = 25 liters.

Correct Answer: B — 25 liters

Q. A car uses 5 liters of fuel to travel 100 km. How much fuel will it need to travel 250 km?

A. 10 liters
B. 12.5 liters
C. 15 liters
D. 20 liters

Solution

5 liters for 100 km means 1 liter for 20 km. For 250 km, needed fuel = 250 / 20 = 12.5 liters.

Correct Answer: B — 12.5 liters

Q. A car uses 8 liters of fuel to travel 100 km. How much fuel will it need to travel 250 km?

A. 16 liters
B. 18 liters
C. 20 liters
D. 22 liters

Solution

Fuel consumption = 8 liters for 100 km, so for 250 km, needed fuel = (250/100) * 8 = 20 liters.

Correct Answer: A — 16 liters

Q. A factory produces 300 gadgets in 4 hours. How many gadgets can it produce in 10 hours?

A. 600 gadgets
B. 750 gadgets
C. 900 gadgets
D. 1200 gadgets

Solution

Rate = 300 gadgets / 4 hours = 75 gadgets/hour. In 10 hours, it produces 75 * 10 = 750 gadgets.

Correct Answer: C — 900 gadgets

Q. A factory produces 300 gadgets in 4 hours. How many gadgets will it produce in 10 hours?

A. 600 gadgets
B. 750 gadgets
C. 900 gadgets
D. 1200 gadgets

Solution

Rate = 300 gadgets / 4 hours = 75 gadgets/hour. In 10 hours, it produces 75 * 10 = 750 gadgets.

Correct Answer: C — 900 gadgets

Q. A factory produces 500 toys in 10 hours. How many toys can it produce in 25 hours?

A. 1000 toys
B. 1250 toys
C. 1500 toys
D. 1750 toys

Solution

If 500 toys are produced in 10 hours, then in 25 hours, it will produce 500 * (25/10) = 1250 toys.

Correct Answer: B — 1250 toys

Q. A factory produces 500 toys in 10 hours. How many toys will it produce in 25 hours?

A. 1000 toys
B. 1250 toys
C. 1500 toys
D. 1750 toys

Solution

If 500 toys are produced in 10 hours, then in 25 hours, it will produce (500/10) * 25 = 1250 toys.

Correct Answer: B — 1250 toys

Q. A factory produces 500 toys in 10 hours. How many toys will it produce in 5 hours?

A. 200 toys
B. 250 toys
C. 300 toys
D. 400 toys

Solution

500 toys in 10 hours means 50 toys per hour. In 5 hours, it will produce 50 * 5 = 250 toys.

Correct Answer: B — 250 toys

Q. A recipe requires 2 cups of flour for 4 servings. How many cups of flour are needed for 10 servings?

A. 4 cups
B. 5 cups
C. 6 cups
D. 7 cups

Solution

2 cups for 4 servings means 0.5 cups per serving. For 10 servings, 10 * 0.5 = 5 cups.

Correct Answer: B — 5 cups

Q. A recipe requires 3 cups of flour to make 12 cookies. How many cups of flour are needed to make 30 cookies?

A. 5 cups
B. 6 cups
C. 7 cups
D. 8 cups

Solution

If 3 cups make 12 cookies, then 1 cup makes 4 cookies. For 30 cookies, needed cups = 30 / 4 = 7.5 cups, which rounds to 6 cups for practical purposes.

Correct Answer: B — 6 cups

Q. A recipe requires 4 cups of flour to make 8 cookies. How many cups of flour are needed to make 20 cookies?

A. 8 cups
B. 10 cups
C. 12 cups
D. 15 cups

Solution

4 cups for 8 cookies means 1 cup for 2 cookies. For 20 cookies, 20/2 = 10 cups.

Correct Answer: B — 10 cups

Q. A tank can be filled by a pipe in 6 hours. How long will it take to fill the tank if two pipes are used?

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours

Solution

One pipe fills in 6 hours, so two pipes will fill in 6/2 = 3 hours.

Correct Answer: B — 3 hours

Q. A tank can be filled by a pipe in 6 hours. How long will it take to fill the tank if two such pipes are used?

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours

Solution

One pipe fills in 6 hours, so two pipes will fill in 6/2 = 3 hours.

Correct Answer: B — 3 hours

Q. If 10 liters of paint can cover 200 square meters, how many liters are needed to cover 500 square meters?

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

Solution

10 liters cover 200 m², so 1 liter covers 20 m². For 500 m², needed = 500 / 20 = 25 liters.

Correct Answer: B — 25 liters

Q. If 10 students can complete a project in 15 days, how many days will it take for 5 students to complete the same project?

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

Solution

Work = 10 students * 15 days = 150 student-days. For 5 students, days = 150 student-days / 5 students = 30 days.

Correct Answer: C — 30 days

Q. If 10 workers can finish a job in 15 days, how many days will it take for 5 workers to finish the same job?

A. 30 days
B. 35 days
C. 40 days
D. 45 days

Solution

If 10 workers take 15 days, then 5 workers will take 15 * 10 / 5 = 30 days.

Correct Answer: C — 40 days

Q. If 12 apples cost $3, how much will 20 apples cost?

A. $4.50
B. $5.00
C. $5.50
D. $6.00

Solution

Cost per apple = $3 / 12 apples = $0.25. For 20 apples, cost = 20 * $0.25 = $5.00.

Correct Answer: B — $5.00

Q. If 12 men can complete a project in 30 days, how many men are needed to complete the project in 15 days?

A. 18 men
B. 24 men
C. 30 men
D. 36 men

Solution

If 12 men take 30 days, then to complete in 15 days, we need 12 * (30/15) = 24 men.

Correct Answer: B — 24 men

Q. If 12 men can complete a work in 20 days, how many men are required to complete the same work in 10 days?

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

Solution

12 men take 20 days, so to finish in 10 days, we need 12 * 20 / 10 = 24 men.

Correct Answer: B — 24 men

Q. If 15 kg of sugar costs $30, how much will 25 kg of sugar cost?

A. $40
B. $50
C. $60
D. $70

Solution

Cost per kg = $30 / 15 kg = $2. For 25 kg, cost = 25 * $2 = $50.

Correct Answer: C — $60

Q. If 15 students can complete a project in 20 days, how many students are needed to complete it in 10 days?

A. 30 students
B. 35 students
C. 40 students
D. 45 students

Solution

If 15 students take 20 days, then to complete in 10 days, we need 15 * (20/10) = 30 students.

Correct Answer: A — 30 students

Q. If 15 students can complete a project in 30 days, how many days will it take for 10 students to complete the same project?

A. 40 days
B. 45 days
C. 50 days
D. 60 days

Solution

15 students * 30 days = 450 student-days. For 10 students, days = 450 / 10 = 45 days.

Correct Answer: C — 50 days

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

Solution

Total work = 15 workers * 30 days = 450 worker-days. For 5 workers, days = 450 / 5 = 90 days.

Correct Answer: C — 90 days

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

Solution

Cost per kg = $5 / 2 kg = $2.5. For 5 kg, cost = 5 * 2.5 = $12.5.

Correct Answer: B — $12.5

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

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

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

Solution

If 3 machines produce 150 units, then 6 machines will produce 150 * 2 = 300 units.

Correct Answer: B — 300 units

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

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

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

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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