This MCQ module is based on: Percentages – Chapter Exercises
TOPIC 4 OF 23
Percentages – Chapter Exercises
🎓 Class 8
Mathematics
CBSE
Theory
Ch 1 — Percentages
⏱ ~35 min
🌐 Language: [gtranslate]
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This mathematics assessment will be based on: Percentages – Chapter Exercises
Targeting Class 8 level in General Mathematics, with Basic difficulty.
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Figure it Out (Final Exercises)
Q1. The population of Bengaluru in 2025 is about 250% of its population in 2000. If the population in 2000 was 50 lakhs, what is the population in 2025?
\(250\% \times 50 = \frac{250}{100} \times 50 = 2.5 \times 50 = \mathbf{125}\) lakhs (1.25 crore).
Q2. The population of the world in 2025 is about 8.2 billion. Match countries to their approximate % share of world population.
| Country | Population | Options |
|---|---|---|
| Germany | 83 million | 13%, 8%, 18%, 10%, 1%, 35%, 2%, 0.1% |
| India | 1.46 billion | |
| Bangladesh | 175 million | |
| USA | 347 million |
Germany: \(\frac{83}{8200} \times 100 \approx 1\%\)
India: \(\frac{1460}{8200} \times 100 \approx 18\%\)
Bangladesh: \(\frac{175}{8200} \times 100 \approx 2\%\)
USA: \(\frac{347}{8200} \times 100 \approx 4\%\) (closest option depends on choices provided)
India: \(\frac{1460}{8200} \times 100 \approx 18\%\)
Bangladesh: \(\frac{175}{8200} \times 100 \approx 2\%\)
USA: \(\frac{347}{8200} \times 100 \approx 4\%\) (closest option depends on choices provided)
Q3. The price of a mobile phone is ₹8,250. A GST of 18% is added to the price. Which of the following gives the final price of the phone including the GST?
(i) 8250 × 18 (ii) 8250 + 1800 (iii) 8250 × \(\frac{18}{100}\) (iv) 8250 × 18 (v) 8250 × 1.18 (vi) 8250 + 8250 × 0.18 (vii) 1.8 × 8250
(i) 8250 × 18 (ii) 8250 + 1800 (iii) 8250 × \(\frac{18}{100}\) (iv) 8250 × 18 (v) 8250 × 1.18 (vi) 8250 + 8250 × 0.18 (vii) 1.8 × 8250
GST = \(18\% \times 8250 = 0.18 \times 8250 = ₹1485\). Final price = \(8250 + 1485 = ₹9735\).
(v) 8250 × 1.18 = 9735 ✓
(vi) 8250 + 8250 × 0.18 = 8250 + 1485 = 9735 ✓
Both (v) and (vi) give the correct final price.
(v) 8250 × 1.18 = 9735 ✓
(vi) 8250 + 8250 × 0.18 = 8250 + 1485 = 9735 ✓
Both (v) and (vi) give the correct final price.
Q4. The monthly percentage change in population of mice in a lab: Month 1 = +5%, Month 2 = −2%, Month 3 = −3%. The initial population is \(p\). Which statements are true?
(i) Population after 3 months = \(p \times 0.05 \times 0.02 \times 0.03\)
(ii) Population after 3 months = \(p \times 1.05 \times 0.98 \times 0.97\)
(iii) Population after 3 months = \(p + 0.05 - 0.02 - 0.03\)
(iv) Population after 3 months was \(p\)
(v) Population after 3 months was more than \(p\)
(vi) Population after 3 months was less than \(p\)
(i) Population after 3 months = \(p \times 0.05 \times 0.02 \times 0.03\)
(ii) Population after 3 months = \(p \times 1.05 \times 0.98 \times 0.97\)
(iii) Population after 3 months = \(p + 0.05 - 0.02 - 0.03\)
(iv) Population after 3 months was \(p\)
(v) Population after 3 months was more than \(p\)
(vi) Population after 3 months was less than \(p\)
(ii) is correct: Population = \(p \times 1.05 \times 0.98 \times 0.97 = p \times 0.99813\).
Since \(0.99813 < 1\), the population decreased slightly. (vi) is true — population is slightly less than \(p\).
(i) is wrong (multiplies the changes, not the factors). (iii) adds them to \(p\), not multiplying. (iv) says exactly \(p\) — wrong since \(0.99813 \ne 1\). (v) is wrong since \(< 1\).
Since \(0.99813 < 1\), the population decreased slightly. (vi) is true — population is slightly less than \(p\).
(i) is wrong (multiplies the changes, not the factors). (iii) adds them to \(p\), not multiplying. (iv) says exactly \(p\) — wrong since \(0.99813 \ne 1\). (v) is wrong since \(< 1\).
Q5. A shopkeeper initially set the price of a product with a 35% profit margin. Due to poor sales, he decided to offer a 30% discount on the selling price. Will he make a profit or a loss? Give reasons.
Let CP = 100. With 35% profit: SP = 135. After 30% discount: New SP = \(135 \times 0.70 = 94.5\).
Since New SP (94.5) < CP (100), he makes a loss of 5.5%.
This is because successive changes are multiplicative: \(1.35 \times 0.70 = 0.945 < 1\).
Since New SP (94.5) < CP (100), he makes a loss of 5.5%.
This is because successive changes are multiplicative: \(1.35 \times 0.70 = 0.945 < 1\).
Q6. What percentage of area is occupied by the region marked 'E' in the figure?
The figure is a 4×4 grid (16 squares total). Region E occupies 3 squares (L-shape).
Percentage = \(\frac{3}{16} \times 100 = 18.75\%\).
Percentage = \(\frac{3}{16} \times 100 = 18.75\%\).
Q7. A number increased by 20% becomes 90. What is the number?
\(x \times 1.20 = 90\), so \(x = \frac{90}{1.20} = \mathbf{75}\).
Q8. The population of elephants in a national park increased by 5% in the last decade. If the population of the elephants last decade is \(p\), the population now is:
(i) \(p \times 0.5\) (ii) \(p \times 0.05\) (iii) \(p \times 1.5\) (iv) \(p \times 1.05\) (v) \(p \times 1.50\)
(i) \(p \times 0.5\) (ii) \(p \times 0.05\) (iii) \(p \times 1.5\) (iv) \(p \times 1.05\) (v) \(p \times 1.50\)
(iv) \(p \times 1.05\) — a 5% increase means the new population is 105% of the original, which is \(p \times 1.05\).
Q9. Which statement(s) mean the same as — "The demand for cameras has fallen by 85% in the last decade"?
(i) The demand now is 85% of the demand a decade ago.
(ii) The demand a decade ago was 85% of the demand now.
(iii) The demand now is 15% of the demand a decade ago.
(iv) The demand a decade ago was 15% of the demand now.
(v) The demand a decade ago was 185% of the demand now.
(vi) The demand now is 185% of the demand a decade ago.
(i) The demand now is 85% of the demand a decade ago.
(ii) The demand a decade ago was 85% of the demand now.
(iii) The demand now is 15% of the demand a decade ago.
(iv) The demand a decade ago was 15% of the demand now.
(v) The demand a decade ago was 185% of the demand now.
(vi) The demand now is 185% of the demand a decade ago.
"Fallen by 85%" means demand now = \(100\% - 85\% = 15\%\) of original.
(iii) is correct: demand now = 15% of decade ago.
(i) says 85% — wrong, that would be "fallen by 15%".
(v): decade ago vs now: if now = 0.15 × old, then old = \(\frac{1}{0.15} \times\) now = 6.67 × now = 667%. Not 185%.
Only (iii) is correct.
(iii) is correct: demand now = 15% of decade ago.
(i) says 85% — wrong, that would be "fallen by 15%".
(v): decade ago vs now: if now = 0.15 × old, then old = \(\frac{1}{0.15} \times\) now = 6.67 × now = 667%. Not 185%.
Only (iii) is correct.
Q14. In a room of 100 people, 99% are left-handed. How many left-handed people have to leave the room to bring that percentage down to 98%?
Currently: 99 left-handed, 1 right-handed. We want left-handed to be 98% of the remaining people.
If \(x\) left-handed people leave: \(\frac{99-x}{100-x} = 0.98\).
\(99 - x = 0.98(100 - x) = 98 - 0.98x\).
\(99 - x = 98 - 0.98x\) → \(1 = 0.02x\) → \(x = 50\).
50 left-handed people must leave! (Counter-intuitive but correct.)
If \(x\) left-handed people leave: \(\frac{99-x}{100-x} = 0.98\).
\(99 - x = 0.98(100 - x) = 98 - 0.98x\).
\(99 - x = 98 - 0.98x\) → \(1 = 0.02x\) → \(x = 50\).
50 left-handed people must leave! (Counter-intuitive but correct.)
Q15. Look at the horizontal bar chart showing computer literacy by age and gender. Which statements are valid?
(i) People in their twenties are the most computer-literate across all age groups.
(ii) Women lag behind in ability to use computers across age groups.
(iii) There are more people in their twenties than teenagers.
(iv) More than a quarter of people in their thirties can use computers.
(v) Less than 1 in 10 aged 60 and above can use computers.
(vi) Half of the people in their twenties can use computers.
(i) People in their twenties are the most computer-literate across all age groups.
(ii) Women lag behind in ability to use computers across age groups.
(iii) There are more people in their twenties than teenagers.
(iv) More than a quarter of people in their thirties can use computers.
(v) Less than 1 in 10 aged 60 and above can use computers.
(vi) Half of the people in their twenties can use computers.
Source: NSS Round 79, Comprehensive Annual Modular Survey, National Statistics Office
(i) True — Twenties have the highest bars (26% female, 37% male).
(ii) True — Female bars are shorter than male bars across all age groups.
(iii) Cannot be determined — the chart shows percentages within each age group, not absolute population sizes.
(iv) True — 25% male in thirties = exactly a quarter. Combining both genders, more than a quarter can use computers.
(v) True — Seniors: 3% female, 4% male — both under 10%.
(vi) False — Twenties: 26% female, 37% male — neither is 50%.
(ii) True — Female bars are shorter than male bars across all age groups.
(iii) Cannot be determined — the chart shows percentages within each age group, not absolute population sizes.
(iv) True — 25% male in thirties = exactly a quarter. Combining both genders, more than a quarter can use computers.
(v) True — Seniors: 3% female, 4% male — both under 10%.
(vi) False — Twenties: 26% female, 37% male — neither is 50%.
Chapter Summary
- Percentages are widely used in our daily life. They are fractions with denominator 100. \(x\% = \frac{x}{100}\).
- Fractions can be converted to percentages and vice versa. Decimals too can be converted to percentages and vice versa. For example, \(\frac{2}{5} = 0.4 = 40\%\).
- We have learnt to find the exact number when a certain percentage of the total quantity is given.
- When parts of a quantity are given to us as ratios, we have seen how to convert them to percentages.
- The increase or decrease in a certain quantity can also be expressed as a percentage increase/decrease.
- The profits or losses incurred in transactions, and tax rates, can be expressed in terms of percentages.
- We have seen how a quantity or a number grows when compounded. Interest rates are a common example. If \(p\) is the principal, \(r\) is the rate, and \(t\) is the number of terms:
Without compounding: \(p \times (1 + rt)\) — the principal remains the same.
With compounding: \(p \times (1 + r)^t\) — the principal grows each term.
- A situation or a problem can often be solved by describing it using a rough diagram. We have learnt to estimate and do mental computations to solve problems related to percentages.
Puzzle: Peaceful Knights
Place 8 knights on the chess board so that no knight attacks another. A knight moves in an 'L-shape': either (a) two steps vertically and one step horizontally, or (b) two steps horizontally and one step vertically.
8×8 chessboard — a knight's L-shaped move pattern is shown on page 32 of the PDF
Need a hint?
Hint: Think about which squares a knight on a white square can attack — they're always dark squares, and vice versa! So if you place all 8 knights on the same colour, they can never attack each other.
Solution: One simple solution: place all 8 knights on the first row (a1, b1, c1, d1, e1, f1, g1, h1). No knight in the same row can attack another knight in the same row using an L-shaped move. Many other solutions exist — for example, placing them all on the 8 squares of one diagonal.
Solution: One simple solution: place all 8 knights on the first row (a1, b1, c1, d1, e1, f1, g1, h1). No knight in the same row can attack another knight in the same row using an L-shaped move. Many other solutions exist — for example, placing them all on the 8 squares of one diagonal.
Activity: Percentage in Your Daily Life
L3 Apply
Challenge: Can you find 10 different examples of percentages being used around you in one day?
- Over one day, note every time you see a percentage mentioned — on food labels, ads, news, shops, report cards, weather forecasts, etc.
- For each, classify it: is it used for comparison, profit/loss, growth, composition, or probability?
- Pick 3 examples and verify the calculation. Does the percentage make sense given the context?
Examples you might find:
- Battery: 73% charged (composition)
- Sale: 40% off on shoes (discount)
- Milk packet: 3.5% fat (composition)
- Cricket: win probability 65% (probability)
- News: GDP grew by 6.5% (growth)
- Report card: 88% in Maths (comparison)
Competency-Based Questions
Scenario: A school has 1200 students. In 2024, 60% of students passed with first division. In 2025, the school improved and 72% passed with first division. The total number of students remained the same.
Q1. How many more students got first division in 2025 than in 2024?
L3 ApplyAnswer: (c) 144. 2024: \(60\% \times 1200 = 720\). 2025: \(72\% \times 1200 = 864\). Difference = \(864 - 720 = 144\).
Q2. The percentage increase from 60% to 72% is 12 percentage points. But what is the percentage increase in the number of first-division students? Analyse the difference.
L4 AnalyseAnswer: Increase = 144 students. Percentage increase = \(\frac{144}{720} \times 100 = 20\%\).
The percentage-point increase is 12 (from 60% to 72%), but the percentage increase in the count is 20% (from 720 to 864). These are different concepts — percentage points vs relative percentage change.
The percentage-point increase is 12 (from 60% to 72%), but the percentage increase in the count is 20% (from 720 to 864). These are different concepts — percentage points vs relative percentage change.
Q3. If the school's total strength grew by 10% in 2026 (to 1320) but the first-division rate dropped back to 60%, evaluate whether the school actually has more or fewer first-division students than in 2025.
L5 EvaluateAnswer: 2026: \(60\% \times 1320 = 792\). 2025: 864. Since \(792 < 864\), the school has fewer first-division students in 2026 despite having more total students. The rate drop (72% → 60%) outweighed the population growth (1200 → 1320).
Q4. Design a target: if the school wants at least 900 first-division students in 2027 with an expected strength of 1350, what minimum percentage pass rate is needed?
L6 CreateAnswer: Need: \(x\% \times 1350 \ge 900\). So \(x \ge \frac{900}{1350} \times 100 = 66.\overline{6}\%\). The school needs a minimum pass rate of approximately 66.7% (or \(66\frac{2}{3}\%\)) to achieve 900 first-division students.
Assertion–Reason Questions
Assertion (A): 99 out of 100 people in a room are left-handed. To make it 98%, exactly 50 left-handed people must leave.
Reason (R): When the total changes, the percentage calculation changes non-linearly.
Reason (R): When the total changes, the percentage calculation changes non-linearly.
Answer: (a) — Both true. After 50 leave: 49 left-handed out of 50 total = 98%. R explains the counter-intuitive result: as people leave, the denominator shrinks, making it harder to reduce the percentage.
Assertion (A): A price increased by 10% and then decreased by 10% returns to the original price.
Reason (R): \(+10\% - 10\% = 0\%\) net change.
Reason (R): \(+10\% - 10\% = 0\%\) net change.
Answer: (d) — Both are false. If original = 100: after +10% = 110. After −10% of 110 = 110 − 11 = 99. The price is 99, not 100. The net change is −1%. R's reasoning (+10 −10 = 0) is wrong because successive changes are multiplicative: \(1.1 \times 0.9 = 0.99\).
Frequently Asked Questions — Chapter 1
What is Percentages - Chapter Exercises in NCERT Class 8 Mathematics?
Percentages - Chapter Exercises is a key concept covered in NCERT Class 8 Mathematics, Chapter 1: Chapter 1. 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 Percentages - Chapter Exercises step by step?
To solve problems on Percentages - Chapter 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 1: Chapter 1?
The essential formulas of Chapter 1 (Chapter 1) 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 Percentages - Chapter Exercises important for the Class 8 board exam?
Percentages - Chapter 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 Percentages - Chapter Exercises?
Common mistakes in Percentages - Chapter 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 Percentages - Chapter Exercises?
End-of-chapter NCERT exercises for Percentages - Chapter 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 1, and solve at least one previous-year board paper to consolidate your understanding.
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