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Class 8 Maths Chapter 1 Fractions in Disguise NCERT Solutions | Ganita Prakash Part 2 Complete Explanation

 Class 8 Maths Chapter 1 Fractions in Disguise NCERT Solutions | Ganita Prakash Part 2 Complete Explanation

Introduction

“Fractions in Disguise” is Chapter 1 of Ganita Prakash Part-II (Class 8). It shows how percentages are simply fractions with denominator 100. You will learn to convert fractions ↔ percentages, find percentage of a quantity, compare scores/proportions, calculate profit-loss, discounts, taxes, and even compound interest. The chapter uses bar models, real-life examples (biscuits, paint, sales targets) and multiple methods to build deep understanding.

Basic Knowledge Required

  • What is a fraction?
  • Equivalent fractions
  • Multiplication of fraction by whole number
  • Bar models / number lines
  • Simple ratio & proportion

Key Definitions

  • Per cent (%) = “per hundred” = fraction with denominator 100.
  • y% y\% of x x = y100×x \dfrac{y}{100} \times x
  • Fraction to percentage: multiply by 100.
  • Percentage to fraction: y100 \dfrac{y}{100} (simplify if possible).

Important Formulas Used

  1. Fraction → Percentage: ab×100% \dfrac{a}{b} \times 100\%
  2. Percentage of quantity: y100×x \dfrac{y}{100} \times x
  3. Percentage increase/decrease: changeoriginal×100 \dfrac{\text{change}}{\text{original}} \times 100
  4. Profit % = SP−CPCP×100 \dfrac{\text{SP} - \text{CP}}{\text{CP}} \times 100
  5. Loss % = CP−SPCP×100 \dfrac{\text{CP} - \text{SP}}{\text{CP}} \times 100
  6. Discount/Sale price = Marked Price × (1 – discount rate)
  7. Amount after simple interest (no compounding): Principal + (Principal × rate × time)
  8. Compound interest (annual): A=P×(1+r)n A = P \times (1 + r)^n

1.1 Fractions as Percentages – All Solved Examples & Figure it Out

Example 1 (Red paint in orange colour) 34=75100=75% \dfrac{3}{4} = \dfrac{75}{100} = 75\% Yellow = 25% 25\%

Example 2 (Save 25 \dfrac{2}{5} ) 25×100=40% \dfrac{2}{5} \times 100 = 40\%

Example 3 (24% as fraction) 24%=24100=625 24\% = \dfrac{24}{100} = \dfrac{6}{25}

Figure it Out 1

(i) 35×100=60% \dfrac{3}{5} \times 100 = 60\% (ii) 714=12=50% \dfrac{7}{14} = \dfrac{1}{2} = 50\% (iii) 920×100=45% \dfrac{9}{20} \times 100 = 45\% (iv) 72150=48% \dfrac{72}{150} = 48\% (v) 13×100≈33.33% \dfrac{1}{3} \times 100 \approx 33.33\% (vi) 511×100≈45.45% \dfrac{5}{11} \times 100 \approx 45.45\%

Figure it Out 2

15 white out of 25 = 1525×100=60% \dfrac{15}{25} \times 100 = 60\% → (vi) None of these

Figure it Out 3

15 out of 80 = 1580×100=18.75% \dfrac{15}{80} \times 100 = 18.75\%

Figure it Out 4

(Visual runners) – Match given % directly from diagram.

Figure it Out 5

(i) 50% > 5% (ii) 510=50% \dfrac{5}{10} = 50\% → = (iii) 311≈27.27%<61% \dfrac{3}{11} \approx 27.27\% < 61\% (iv) 30% < 13≈33.33% \dfrac{1}{3} \approx 33.33\%

1.2 Percentage of Some Quantity – All Solved Examples & Figure it Out

Example 1 (Sugar in biscuits) Madhu: 25% of 120 g = 25100×120=30 \dfrac{25}{100} \times 120 = 30 g Madhav: 35% of 95 g = 33.25 g → Madhav ate more sugar.

Free-hand Computations Table (mental maths answers) 25% row: 25, 50, 12.5, 20, 2.5, 8.75, 71.75 10% row: 10, 20, 5, 8, 1, 3.5, 28.7 20% row: 20, 40, 10, 16, 2, 7, 57.4 5% row: 5, 10, 2.5, 4, 0.5, 1.75, 14.35

FDP Trio Table 50% → 12 \dfrac{1}{2} , 0.5 100% → 1, 1 25% → 14 \dfrac{1}{4} , 0.25 75% → 34 \dfrac{3}{4} , 0.75 10% → 110 \dfrac{1}{10} , 0.1 1% → 1100 \dfrac{1}{100} , 0.01 5% → 120 \dfrac{1}{20} , 0.05 43% → 43100 \dfrac{43}{100} , 0.43

Example 3 (A grade) 80% of 75 = 60 marks

Example 4 (Millet kanji) 29×100≈22.22% \dfrac{2}{9} \times 100 \approx 22.22\% millet 500 ml → 111.1 ml millet

Example 5 (Cyclist Delhi-Agra) Total distance = 230 km → remaining 138 km

Example 6 (Sales target >100%) Day 4: 120% Day 5: 156% Day 6: 191% Day 7: 150% → ₹7500 Day 8: 210% → ₹10,500

Example 7 (Wheat harvest) 650260×100=250% \dfrac{650}{260} \times 100 = 250\%

Figure it Out 1 (Missing numbers)

(i) 20% of 100 = 20 → blanks 20, 40, 60, 80 (ii) 75% of 60 = 45 → 15, 30, 45, 60 (iii) 140% of 100 = 140 → 20, 40, 60, 80, 100, 120, 140 (iv) 90 (given)

Figure it Out 2

(i) 25% of 160 = 40 (ii) 16% of 250 = 40 (iii) 62% of 360 = 223.2 (iv) 140% of 40 = 56 (v) 1% of 1 h = 0.6 min (vi) 7% of 10 kg = 0.7 kg

Figure it Out 3

60 ml paint, 34 \dfrac{3}{4} red → 45 ml red

Figure it Out 4

(i) = (both same) (ii) 37% < 73% (iii) 29% of 43 < 92% of 110 (iv) = (v) 45% of 200 > 10% of 490 (vi) =

Figure it Out 5

(i) 140, 210, 280 (ii) 21.5, 2.15, 12.9 (iii) 24.3, 48.6, 300

Figure it Out 6

(i) 1% (ii) 1.6 (iii) 50

Figure it Out 7

10% of day = 2.4 h 1% of week = 1.68 h → 10% day is longer

Figure it Out 8

Day 1: 50%, Day 2: ≈66.67%, … Day 99: 99% Pattern: bull eats (n-1)% of fodder given on day n.

Figure it Out 9

18 days for 20% → 90 days for 100%

Figure it Out 10

Warm-up: 9 min, Play: 72 min, Cool-down: 9 min

Figure it Out 11

≈7.2 billion (approx.)

Figure it Out 12

(i) Same proportions (ii) Rava 0.8 kg, Sugar 0.8 kg, Ghee 0.4 kg

1.3 Using Percentages – All Solved Examples & Figure it Out

Example 1 (Eesha scores) English 84%, Science 87.5% → Science better

Example 2 (Badam mix) DEF: Badam 10%, Zacni: Badam 20% → Zacni has more badam

Percentage Increase/Decrease Tomatoes: 40% increase Footfall: 37.5% decrease

Profit & Loss Kishanlal profit 43.33% Raghu loss 14.28% Shyamala sale ₹2173

Figure it Out

  1. Profit margin = 3575×100≈46.67% \dfrac{35}{75} \times 100 \approx 46.67\%
  2. Selling price = ₹712.5
  3. Expenditure = ₹1.875 crore
  4. Anwar pays ₹225
  5. (ii) 66.67% increase

Growth & Compounding Option 1 (no compounding): ₹7800 Option 2 (compounding): ₹7986

Figure it Out 1 (Bank of Yahapur)

Without compounding: ₹24,200 With compounding: ₹24,620


15 Most Asked FAQs – Fractions in Disguise (Click to Expand)

1. Express 3/4 as percentage.

Answer: \(\frac{3}{4} \times 100 = 75\%\)

2. What percentage is 15 white marbles out of 25?

Answer: \(\frac{15}{25} \times 100 = 60\%\)

3. Find 25% of 120 g biscuits (sugar content).

Answer: \(\frac{25}{100} \times 120 = 30\) g

4. How much millet in 500 ml kanji (2:7 ratio)?

Answer: \(\frac{2}{9} \times 500 \approx 111.1\) ml millet

5. Cyclist covered 92 km which is 40%. Remaining distance?

Answer: Total distance = 230 km → remaining = 138 km

6. Sales ₹6000 vs target ₹5000. What percentage?

Answer: \(\frac{6000}{5000} \times 100 = 120\%\)

7. 650 kg this year vs 260 kg last year. Percentage of last year’s harvest?

Answer: \(\frac{650}{260} \times 100 = 250\%\)

8. Eesha: 42/50 English, 70/80 Science. Which test did she score better?

Answer: English 84%, Science 87.5% → Science is better

9. Shopkeeper buys geometry box for ₹75 and sells for ₹110. Profit %?

Answer: \(\frac{35}{75} \times 100 \approx 46.67\%\)

10. Petrol price from ₹60 to ₹100. Percentage increase?

Answer: \(\frac{40}{60} \times 100 \approx 66.67\%\)

11. 15% discount on ₹1800 cooker. What is the selling price?

Answer: ₹1800 – 15% = ₹1530

12. Compound interest on ₹6000 @10% p.a. for 3 years?

Answer: ₹7986 (with annual compounding)

13. Is 10% of a day longer than 1% of a week?

Answer: Yes → 10% day = 2.4 hours > 1% week = 1.68 hours

14. Bull eats pattern: Day 1 = 50%, Day 99 = 99%. What is the pattern?

Answer: Bull eats (day number – 1)% of the fodder given that day

15. 90% of world population lives in Northern Hemisphere. Approx. people?

Answer: ≈ 7.2 billion (2025 estimate)

✅ All solutions are step-by-step as per Ganita Prakash Part-II Chapter 1.

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