This MCQ module is based on: Chapter 3 Exercises
TOPIC 10 OF 23
Chapter 3 Exercises
🎓 Class 8
Mathematics
CBSE
Theory
Ch 3 — Direct and Inverse Proportions
⏱ ~35 min
🌐 Language: [gtranslate]
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This mathematics assessment will be based on: Chapter 3 Exercises
Targeting Class 8 level in General Mathematics, with Basic difficulty.
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Figure it Out — Chapter 3 Exercises
Q1. Does the pie chart on the right show the result of a survey carried out to find the modes of transport used by children to go to school. Study the pie chart and answer the questions: (i) most common mode? (ii) what fraction travel by car? (iii) if 18 children travel by car, how many children took part in the survey? (iv) by which two modes of transport are equal numbers travelling? (Angles: Walk 120°, Bus 140°, Car 40°, Cycle 36°, Two-wheeler 24°)
(i) Bus (largest slice, 140°).
(ii) Car fraction = \(40/360 = 1/9\).
(iii) If 18 children = 1/9 of total → total = 162 children.
(iv) None exactly equal in this pie; re-examine slices — closest: Car (40°) and Cycle (36°) are approximately equal. (Answer may vary with the exact pie chart given in NCERT.)
(ii) Car fraction = \(40/360 = 1/9\).
(iii) If 18 children = 1/9 of total → total = 162 children.
(iv) None exactly equal in this pie; re-examine slices — closest: Car (40°) and Cycle (36°) are approximately equal. (Answer may vary with the exact pie chart given in NCERT.)
Q2. Three workers can paint a fence in 4 days. If one more worker joins them, how long will it take to finish the work?
Workers × days = constant. 3 × 4 = 4 × t → t = 3 days.
Q3. It takes 6 hours to fill 2 tanks of the same volume. How long will it take to fill 5 such tanks with the same pump?
Direct proportion: hours/tanks constant = 3. For 5 tanks: 5 × 3 = 15 hours.
Q4. A given set of chairs are arranged in 25 rows, with 12 chairs in each row. If the chairs are rearranged with 20 chairs in each row, how many rows does this new arrangement have?
Inverse proportion (total chairs constant). Total = 25 × 12 = 300. New rows = 300 / 20 = 15 rows.
Q5. A school has 8 periods a day, each of 45 minutes duration. How long will each period be, if the school has 9 periods a day (assuming that the number of school hours per day stays the same)?
Total minutes = 8 × 45 = 360. New duration = 360 ÷ 9 = 40 minutes.
Q6. A small pump can fill a tank in 3 hours, while a large pump can fill the same tank in 2 hours. If both pumps are used together, how long will it take to fill the tank?
Small pump rate = 1/3 tank/hr; large pump rate = 1/2 tank/hr. Combined = 1/3 + 1/2 = 5/6 tank/hr. Time = 6/5 hours = 1 hour 12 min.
Q7. A factory requires 42 machines to produce a given number of toys in 63 days. How many machines are required to produce the same number of toys in 54 days?
Machines × days = constant. 42 × 63 = m × 54 → m = 2646/54 = 49 machines.
Q8. A car takes 2 hours to reach a destination, travelling at a speed of 60 km/h. How long will the car take if it travels at a speed of 80 km/h?
Distance = 60 × 2 = 120 km. Time = 120/80 = 1.5 hours.
Competency-Based Questions (Review)
Scenario: A construction crew uses concrete (cement : sand : gravel = 1 : 1.5 : 3). For a wall, they need 88 bags total. Parallel to this, 5 labourers can finish digging a foundation in 12 days. A surveyor's map has RF 1 : 25,000.
Q1. How many bags of each component does the wall need?
L3Total parts = 5.5. Multiplier = 88/5.5 = 16. Cement = 16, Sand = 24, Gravel = 48.
Q2. If 3 labourers quit on day 4, analyse how many more days remain for the 2 labourers alone.
L45 labourers × 12 days = 60 labour-days total. Completed in 4 days: 5 × 4 = 20 labour-days. Remaining = 40 labour-days. 2 labourers alone: 40/2 = 20 days more.
Q3. Evaluate: "On the RF 1 : 25,000 map, 1 cm represents 2.5 km." Correct?
L51 cm = 25,000 cm = 250 m = 0.25 km. The statement is incorrect — it is 0.25 km, not 2.5 km (off by a factor of 10).
Q4. Create a table that simultaneously shows direct AND inverse proportion scenarios for a school canteen.
L6Direct: Cost ∝ number of samosas. 5 samosas = ₹50, 10 = ₹100, 20 = ₹200. Inverse: Staff hours × staff = constant. 2 staff × 4 hrs = 1 staff × 8 hrs. Multi-variable scenarios strengthen reasoning.
Assertion–Reason Questions
A: When 110 units of concrete are made in ratio 1 : 1.5 : 3, we get 20 units cement, 30 units sand, 60 units gravel.
R: The sum of parts 5.5 divides 110 evenly to give 20 as multiplier.
R: The sum of parts 5.5 divides 110 evenly to give 20 as multiplier.
(a) Both valid; multiplier 20 is used to scale each part.
A: Adding more pumps reduces time to fill a tank, but there's a limit.
R: Inverse proportion is a mathematical idealisation; real systems have constraints.
R: Inverse proportion is a mathematical idealisation; real systems have constraints.
(a) Physical limits (pipe diameter, water pressure) cap practical gains.
Activity: Build Your Own Proportion Problem
Pick two quantities from daily life (e.g., packets of snacks vs. number of guests, or fan speed vs. battery life). Decide whether they are in direct or inverse proportion, collect 4 data points, plot them on graph paper and check if the product or ratio is constant.
Summary
- Ratios in the form \(a : b : c : d\) indicate that for every \(a\) units of the first quantity, there are \(b\) of the second, \(c\) of the third and \(d\) of the fourth.
- If a is divided into many parts in the ratio \(p : q : r : s\), then the quantity of the second part is \(a \times \dfrac{q}{p+q+r+s}\), and so on.
- Two quantities are directly proportional when they change by the same factor. Same relation remains: \(\frac{x_1}{y_1} = \frac{x_2}{y_2} = \ldots = k\), where \(k\) is a constant.
- Quantities are inversely proportional when one quantity changes by a factor and the other changes by the reciprocal factor. Product remains constant: \(x_1 y_1 = x_2 y_2 = \ldots = n\).
- Maps use the Representative Fraction (RF) like 1 : 60,00,000 to link map distance and actual distance.
- Pie charts convert category proportions into slice angles via direct proportion: angle = (fraction) × 360°.
Keywords
Proportional Ratio Multi-term ratio Representative Fraction Direct Proportion Inverse Proportion Constant of Proportionality Pie Chart ScaleFrequently Asked Questions
What exercises are in Class 8 Part 2 Chapter 3?
Chapter 3 exercises include identifying proportion type, finding missing terms, solving direct and inverse word problems (workers-time, speed-time, cost-quantity), and map scale calculations. NCERT Class 8 Ganita Prakash Part 2 gives thorough practice.
How to solve: 6 pipes fill a tank in 1 hour 20 minutes. How long for 5 pipes?
More pipes = less time (inverse proportion). Let time for 5 pipes be t minutes. 6 x 80 = 5 x t, so t = 480/5 = 96 minutes = 1 hour 36 minutes. NCERT Class 8 Chapter 3 exercises include such problems.
What is the summary of Chapter 3?
Key ideas: direct proportion keeps ratio constant (y/x = k); inverse proportion keeps product constant (xy = k); maps use direct proportion; identify proportion type before solving. NCERT Class 8 Ganita Prakash Part 2 Chapter 3.
When is two-variable relationship neither direct nor inverse?
When changing one variable affects the other in a non-proportional way. For example, an object's age and height relationship is monotonic but not proportional. NCERT Class 8 Chapter 3 reminds students to check carefully before applying proportion methods.
Why are Class 8 proportion exercises important?
Proportion problems test reasoning about relationships between quantities - a skill vital in science, business, and further mathematics (similar triangles, percentages, rates). NCERT Class 8 Ganita Prakash Part 2 Chapter 3 builds this.
Can both direct and inverse proportion appear in one problem?
Yes. Compound problems involve three or more variables with mixed direct/inverse relationships, solved step by step or with the unitary method. NCERT Class 8 Chapter 3 introduces simple compound cases in exercises.
Frequently Asked Questions — Chapter 3
What is Chapter 3 Exercises in NCERT Class 8 Mathematics?
Chapter 3 Exercises is a key concept covered in NCERT Class 8 Mathematics, Chapter 3: Chapter 3. This lesson builds the student's foundation in the chapter by explaining the core ideas with worked examples, definitions, and step-by-step methods aligned to the CBSE curriculum.
How do I solve problems on Chapter 3 Exercises step by step?
To solve problems on Chapter 3 Exercises, follow the NCERT method: identify the given quantities, choose the relevant formula or theorem, substitute values carefully, and simplify. Class 8 exercises gradually increase in difficulty — start with solved NCERT examples before attempting exercise questions, and always verify your answer by substitution or diagram.
What are the most important formulas for Chapter 3: Chapter 3?
The essential formulas of Chapter 3 (Chapter 3) are listed in the chapter summary and highlighted throughout the lesson in formula boxes. Memorise them and practise at least 2–3 problems per formula. CBSE board exams frequently test direct application as well as combined use of multiple formulas from this chapter.
Is Chapter 3 Exercises important for the Class 8 board exam?
Chapter 3 Exercises is part of the NCERT Class 8 Mathematics syllabus and appears in CBSE board exams. Questions typically include short-answer, long-answer, and competency-based items. Review the NCERT examples, exercise questions, and previous-year board problems on this topic to prepare confidently.
What mistakes should students avoid in Chapter 3 Exercises?
Common mistakes in Chapter 3 Exercises include skipping steps, misapplying formulas, sign errors, and losing track of units. Write each step clearly, double-check algebraic manipulations, and re-read the question after solving to verify that your answer matches what was asked.
Where can I find more NCERT practice questions on Chapter 3 Exercises?
End-of-chapter NCERT exercises for Chapter 3 Exercises cover all difficulty levels tested in CBSE exams. After completing them, try the examples again without looking at the solutions, attempt the NCERT Exemplar questions for Chapter 3, and solve at least one previous-year board paper to consolidate your understanding.
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