Example 1 (Page 14) - Chapter 1 Class 8 - Fractions in Disguise (Ganita Prakash II)

Transcript

Example 1 (Page 14) Eesha scored 42 marks out of 50 on an English test and 70 marks out of 80 in a Science test. Since she lost only 8 marks in English but 10 marks in Science, she thinks she has done better at English. Reema does not agree! She argues that since Eesha has scored more marks in Science, she has done better at Science. Vishu thinks we cannot compare the scores because the maximum marks are different. Who do you think is correct?This problem is about "Comparing Proportions." It starts with a debate between friends: The Problem: Eesha took two tests. English: She got 42 out of 50. Science: She got 70 out of 80. The Debate: Vishu's Logic: He thinks she did better in English because she only lost 8 marks (50 - 42), whereas in Science she lost 10 marks (80 - 70). Reema's Logic: She disagrees because the total marks are different. You can't compare them directly! To settle this argument, we need to make the totals the same. The best way to do that is to turn both scores into Percentages (scores out of 100). Finding English Percentage Percentage scored in English = (𝑀𝑎𝑟𝑘𝑠 𝑠𝑐𝑜𝑟𝑒𝑑 𝑖𝑛 𝐸𝑛𝑔𝑙𝑖𝑠ℎ)/(𝑇𝑜𝑡𝑎𝑙 𝑚𝑎𝑟𝑘𝑠 𝑖𝑛 𝐸𝑛𝑔𝑙𝑖𝑠ℎ 𝑇𝑒𝑠𝑡) × 100 = 𝟒𝟐/𝟓𝟎 × 100 = 42 × 2 = 84% Finding Science Percentage Percentage scored in Science = (𝑀𝑎𝑟𝑘𝑠 𝑠𝑐𝑜𝑟𝑒𝑑 𝑖𝑛 𝑆𝑐𝑖𝑒𝑛𝑐𝑒)/(𝑇𝑜𝑡𝑎𝑙 𝑚𝑎𝑟𝑘𝑠 𝑖𝑛 𝑆𝑐𝑖𝑒𝑛𝑐𝑒 𝑇𝑒𝑠𝑡) × 100 = 𝟕𝟎/𝟖𝟎 × 100 = 7/8 × 100 = 7/2 × 25 = 175/2 = 87.5% Thus, even though she lost more raw marks in Science, her performance was actually higher in Science (87.5%) than in English (84%).