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Fractions in Disguise – Class 8 Mathematics notes, important questions and MCQs

NCERT Class 8 Mathematics, chapter 8. Notes, key terms, important questions with answers and MCQs.

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Chapter overview

Percentages are fractions with denominator 100. They are used for marks, discounts, profit and loss, and interest.

Percentages

  • x% = x/100; to convert a fraction to %, multiply by 100.
  • Percentage increase/decrease = change / original × 100.
  • Common values: 1/2 = 50%, 1/4 = 25%, 1/5 = 20%, 1/8 = 12.5%.

Applications

  • Profit = SP − CP; Profit % = Profit / CP × 100.
  • Discount = Marked Price − Selling Price; discount % is on MP.
  • Simple interest SI = P × R × T / 100; GST is a percentage added to the price.

Key terms

Percent
per hundred
Cost price
price at which an item is bought
Marked price
price printed on the item before discount

Formulas

  • Profit % = (SP − CP)/CP × 100
  • SI = PRT/100

Important questions with answers

Find 12% of 450.2 marks

12/100 × 450 = 54.

A shopkeeper buys a fan for ₹1,500 and sells it for ₹1,725. Find the profit percent.3 marks

Profit = ₹225. Profit % = 225/1500 × 100 = 15%.

A school had 800 students. The number rose by 10% this year and will rise by 5% next year. Find the number next year. Is the overall increase 15%? Explain.5 marks

This year: 800 + 10% = 880. Next year: 880 + 5% of 880 = 880 + 44 = 924. Overall increase = 124/800 × 100 = 15.5%, not 15%, because the second increase is calculated on the bigger number 880.

Quick revision

  • % means out of 100.
  • 12.5% = 1/8.
  • Discount reduces MP to SP.

Exam tips

  • Profit and loss % are always on CP; discount % is on MP.
  • x% of y = y% of x (8% of 50 = 50% of 8 = 4).

Practice MCQs

  1. 3/4 as a percentage is

    1. 34%
    2. 7.5%
    3. 43%
    4. 75%
    Show answer

    Answer: (d) 75%. 3/4 × 100.

  2. 20% of 150 is

    1. 20
    2. 30
    3. 15
    4. 300
    Show answer

    Answer: (b) 30. 0.2 × 150.

  3. A book bought for ₹200 is sold for ₹250. Profit % is

    1. 20%
    2. 25%
    3. 50%
    4. 30%
    Show answer

    Answer: (b) 25%. 50/200 × 100.

  4. A shirt marked ₹800 is sold at 15% discount. Selling price is

    1. ₹720
    2. ₹680
    3. ₹785
    4. ₹120
    Show answer

    Answer: (b) ₹680. 800 − 120.

  5. 3/8 as a percentage is

    1. 30%
    2. 3.8%
    3. 38%
    4. 37.5%
    Show answer

    Answer: (d) 37.5%. 3/8 × 100.

  6. SI on ₹5000 at 8% per year for 3 years is

    1. ₹1000
    2. ₹1200
    3. ₹400
    4. ₹1500
    Show answer

    Answer: (b) ₹1200. 5000 × 8 × 3/100.

  7. A price rises from ₹40 to ₹50. The percentage increase is

    1. 20%
    2. 25%
    3. 10%
    4. 50%
    Show answer

    Answer: (b) 25%. 10/40 × 100.

  8. An article marked ₹800 is sold at 15% discount. Selling price is

    1. ₹720
    2. ₹680
    3. ₹785
    4. ₹120
    Show answer

    Answer: (b) ₹680. 800 − 120.

All chapters of Class 8 Mathematics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.