Easy Level Worksheet
Part A: Subjective Questions - Very Short Answer (1 Mark Each)
Note: Answer each question with steps and explanation. Write down the answers on sheet and submit to the school subject teacher.
Direct and inverse proportions help us understand how quantities change in relation to each other in everyday situations.
Let's start by understanding the basic concepts of proportions.
1. Define direct proportion.
Two quantities are in direct proportion when
Perfect! In direct proportion, if one quantity doubles, the other also doubles.
2. Write one example from daily life showing direct proportion.
Answer:
3. Define inverse proportion.
Answer:
4. What happens to time taken if speed increases?
Time
Great! If we go faster, we reach sooner - time decreases.
5. If 5 pencils cost ₹10, what is the cost of 10 pencils?
Answer: ₹
Perfect! Double the pencils means double the cost: ₹20.
Drag each scenario to the correct category:
Part A: Section B – Short Answer Questions (2 Marks Each)
1. If 6 m of cloth costs ₹300, find the cost of 9 m of the same cloth.
Cost of 6 m = ₹
Cost of 1 m = 300 ÷ 6 = ₹
Cost of 9 m = 50 × 9 = ₹
Excellent! The cost of 9 m of cloth is ₹450.
2. If 3 men can complete a work in 12 days, how long will 6 men take to complete the same work (assuming same rate)?
This is inverse proportion: More men → Less time
3 men take
Number of men doubled (6 = 2 × 3), so time becomes half
6 men will take = 12 ÷ 2 =
Perfect! 6 men will complete the work in 6 days.
3. 5 kg of rice costs ₹400. Find the cost of 8 kg of rice.
Cost of 5 kg = ₹
Cost of 1 kg = 400 ÷ 5 = ₹
Cost of 8 kg = 80 × 8 = ₹
Great work! 8 kg of rice costs ₹640.
4. A car travels 60 km in 1 hour. How far will it go in 4 hours?
This is direct proportion: More time → More distance
Distance in 1 hour =
Distance in 4 hours = 60 × 4 =
Excellent! The car will travel 240 km in 4 hours.
5. If 10 workers can finish a work in 8 days, find how many days 5 workers will take.
This is inverse proportion: Less workers → More time
10 workers take
Total work = 10 × 8 =
5 workers will take = 80 ÷ 5 =
Perfect! 5 workers will take 16 days to finish the work.
Part B: Objective Questions - Test Your Knowledge!
Answer these multiple choice questions:
6. If 2 men complete a work in 8 days, 4 men will take ___ days.
(a) 16 (b) 8 (c) 4 (d) 2
Correct! More men means less time. 4 men (double) take 4 days (half of 8).
7. If 5 machines fill 10 bottles in a minute, how many bottles can 10 machines fill in the same time?
(a) 5 (b) 10 (c) 15 (d) 20
Perfect! Double the machines means double the bottles: 20 bottles.
8. If x = 2, y = 8 and x = 4, y = 4, then x and y are in ___ proportion.
(a) Direct (b) Inverse (c) Equal (d) None
Excellent! When x doubles (2→4), y halves (8→4). This is inverse proportion.
__{.m-red}9. If number of workers increases, time required _____
(a) increases (b) decreases (c) same (d) doubles
Correct! More workers finish the work faster, so time decreases.
10. If 4 books cost ₹80, what is the cost of 1 book?
(a) ₹5 (b) ₹10 (c) ₹15 (d) ₹20
Perfect! Cost of 1 book = 80 ÷ 4 = ₹20.
🎉 Fantastic Work! You've Mastered Basic Proportions!
Here's what you learned:
Direct Proportion: When one quantity increases, the other increases in the same ratio
- Examples: More items → More cost, More distance → More time
Inverse Proportion: When one quantity increases, the other decreases
- Examples: More speed → Less time, More workers → Less time
Key Formulas:
- Direct: x₁/y₁ = x₂/y₂ (ratio remains constant)
- Inverse: x₁ × y₁ = x₂ × y₂ (product remains constant)
Real-world Applications:
- Shopping (items and cost)
- Travel (speed, distance, time)
- Work (workers and time)
Problem-Solving Steps:
- Identify if it's direct or inverse proportion
- Set up the relationship
- Calculate using unitary method or formula
Understanding proportions helps you solve everyday problems involving quantities that change together!