{"id":162645,"date":"2025-02-15T07:26:32","date_gmt":"2025-02-15T07:26:32","guid":{"rendered":"https:\/\/news.gyankatta.org\/?p=162645"},"modified":"2025-02-16T07:55:41","modified_gmt":"2025-02-16T07:55:41","slug":"class-8-math-comparing-quantities-notes","status":"publish","type":"post","link":"https:\/\/news.gyankatta.org\/?p=162645","title":{"rendered":"Class 8 Math Comparing Quantities Notes"},"content":{"rendered":"

Comparing Quantities – Class 8<\/h1>\n

Hi kids! This chapter is all about Comparing Quantities<\/span>. We’ll learn how to use percentages, calculate profit and loss, and understand simple interest \u2013 all things we use in everyday life!<\/p>\n

\"gyankatta\"<\/p>\n

1. Percentage<\/h2>\n

A percentage is a way of expressing a number as a fraction of 100. The word “percent” means “out of 100”. We use the symbol %.<\/p>\n

\n

Example: 25% means 25 out of 100, or 25\/100, which can be simplified to 1\/4.<\/p>\n<\/div>\n

Converting Fractions to Percentages:<\/h3>\n

Multiply the fraction by 100.<\/p>\n

\n

Example: 1\/2 = (1\/2) * 100 = 50%<\/p>\n<\/div>\n

Converting Percentages to Fractions:<\/h3>\n

Divide the percentage by 100 and simplify.<\/p>\n

\n

Example: 75% = 75\/100 = 3\/4<\/p>\n<\/div>\n

\n

Example: If a shirt costs Rs. 500 and is on sale for 20% off, the discount is (20\/100) * 500 = Rs. 100. The sale price is Rs. 500 – Rs. 100 = Rs. 400.<\/p>\n<\/div>\n

2. Profit and Loss<\/h2>\n

These terms are used in business to describe whether money is gained or lost in a transaction.<\/p>\n

    \n
  • Cost Price (CP):<\/span> The price at which an item is bought.<\/li>\n
  • Selling Price (SP):<\/span> The price at which an item is sold.<\/li>\n
  • Profit:<\/span> SP > CP. Profit = SP – CP<\/li>\n
  • Loss:<\/span> SP < CP. Loss = CP – SP<\/li>\n
  • Profit Percentage:<\/span> (Profit \/ CP) * 100<\/li>\n
  • Loss Percentage:<\/span> (Loss \/ CP) * 100<\/li>\n<\/ul>\n
    \n

    Example: A shopkeeper buys a toy for Rs. 200 and sells it for Rs. 250. The profit is Rs. 250 – Rs. 200 = Rs. 50. The profit percentage is (50\/200) * 100 = 25%.<\/p>\n<\/div>\n

    3. Simple Interest<\/h2>\n

    Simple interest is a method of calculating interest on a principal amount. It’s calculated only on the original principal.<\/p>\n

      \n
    • Principal (P):<\/span> The original amount of money.<\/li>\n
    • Rate (R):<\/span> The percentage of interest per year.<\/li>\n
    • Time (T):<\/span> The number of years.<\/li>\n
    • Simple Interest (SI):<\/span> (P * R * T) \/ 100<\/li>\n
    • Amount (A):<\/span> P + SI<\/li>\n<\/ul>\n
      \n

      Example: If you deposit Rs. 1000 in a bank at a simple interest rate of 5% per year for 3 years, the simple interest earned is (1000 * 5 * 3) \/ 100 = Rs. 150. The total amount after 3 years will be Rs. 1000 + Rs. 150 = Rs. 1150.<\/p>\n<\/div>\n

      These concepts are essential for understanding financial transactions, business deals, and many other real-world situations.<\/p>\n

      Comparing Quantities Quiz – Application Problems<\/h1>\n
      \n

      1. Discount: A shopkeeper offers a 20% discount on a dress marked at Rs. 1500. What is the sale price of the dress?<\/p>\n

      Rs. 1200<\/div>\n
      Discount amount = (20\/100) * 1500 = Rs. 300. Sale price = 1500 – 300 = Rs. 1200.<\/div>\n<\/div>\n
      \n

      2. Profit: A fruit seller buys 10 kg of apples for Rs. 400 and sells them for Rs. 50 per kg. What is the profit percentage?<\/p>\n

      25%<\/div>\n
      Cost Price (CP) = Rs. 400. Selling Price (SP) = 10 kg * Rs. 50\/kg = Rs. 500. Profit = SP – CP = 500 – 400 = Rs. 100. Profit % = (Profit\/CP) * 100 = (100\/400) * 100 = 25%.<\/div>\n<\/div>\n
      \n

      3. Simple Interest: Rohan deposits Rs. 5000 in a bank at a simple interest rate of 6% per annum for 2 years. How much interest will he earn?<\/p>\n

      Rs. 600<\/div>\n
      Simple Interest (SI) = (P * R * T) \/ 100 = (5000 * 6 * 2) \/ 100 = Rs. 600.<\/div>\n<\/div>\n
      \n

      4. Percentage Increase: The population of a town increased from 20,000 to 25,000. What is the percentage increase in population?<\/p>\n

      25%<\/div>\n
      Increase in population = 25,000 – 20,000 = 5,000. Percentage increase = (Increase\/Original Population) * 100 = (5000\/20000) * 100 = 25%.<\/div>\n<\/div>\n
      \n

      5. Loss: A shopkeeper sells a chair for Rs. 800, incurring a loss of 20%. What was the cost price of the chair?<\/p>\n

      Rs. 1000<\/div>\n
      Let CP be x. SP = CP – (Loss %) of CP. 800 = x – (20\/100)x. 800 = (80\/100)x. x = (800 * 100) \/ 80 = Rs. 1000.<\/div>\n<\/div>\n
      \n

      6. Percentage Decrease: The price of a car decreased from Rs. 500,000 to Rs. 450,000. What is the percentage decrease in price?<\/p>\n

      10%<\/div>\n
      Decrease in price = 500,000 – 450,000 = 50,000. Percentage decrease = (Decrease\/Original Price) * 100 = (50,000\/500,000) * 100 = 10%.<\/div>\n<\/div>\n
      \n

      7. Profit and Loss: A vendor buys 5 dozen bananas for Rs. 200. He sells each banana for Rs. 5. What is his profit or loss percentage?<\/p>\n

      50% profit<\/div>\n
      5 dozen bananas = 5 * 12 = 60 bananas. CP = Rs. 200. SP = 60 * Rs. 5 = Rs. 300. Profit = 300 – 200 = Rs. 100. Profit % = (100\/200) * 100 = 50%.<\/div>\n<\/div>\n
      \n

      8. Simple Interest Calculation: What principal amount will earn Rs. 900 as simple interest in 3 years at a rate of 5% per annum?<\/p>\n

      Rs. 6000<\/div>\n
      SI = (P * R * T) \/ 100. 900 = (P * 5 * 3) \/ 100. P = (900 * 100) \/ (5 * 3) = Rs. 6000.<\/div>\n<\/div>\n
      \n

      9. Successive Discounts: A shop offers a 10% discount followed by a 20% discount. What is the equivalent single discount?<\/p>\n

      28%<\/div<\/p>\n
      Let the marked price be Rs. 100. After the first discount (10%), the price becomes Rs. 90. After the second discount (20% of Rs. 90), the price becomes Rs. 72. Total discount = 100 – 72 = Rs. 28. Equivalent discount percentage = (28\/100) * 100 = 28%.<\/div>\n<\/div>\n
      \n

      10. Commission: A salesperson receives a 5% commission on all sales. If they sell goods worth Rs. 20,000, what is their commission amount?<\/p>\n

      Rs. 1000<\/div>\n
      Commission = (5\/100) * 20,000 = Rs. 1000.<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

      Comparing Quantities – Class 8 Hi kids! This chapter is all about Comparing Quantities. We’ll learn how to use percentages, calculate profit and loss, and understand simple interest \u2013 all things we use in everyday life! 1. 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