Question 10 - Figure it out - Page 28, 29, 30 - Chapter 1 Class 8 - Fractions in Disguise (Ganita Prakash II)

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Question 10 The bus fares were increased by 3% last year and by 4% this year. What is the overall percentage price increase in the last 2 years?Let Initial Bus fare = b Note: We can assume 100 and solve also – it will be easier that way After Year 1 Fares were increased by 3% last year Thus, Fare after Year 1 = Initial Fare + Change in Fare = Initial Fare + 3% of Initial Fare = b + 3/100 × b = b + 0.03b = b(1 + 0.03) = b × 1.03 After Year 2 Fares were increased by 4% this year Thus, Fare after Year 2 = Fare after Year 1 + Change in Fare = Fare after Year 1 + 4% of Fare after Year 1 = (b × 1.03) + 4/100 × (b × 1.03) = (b × 1.03) × (1 + 𝟒/𝟏𝟎𝟎) = (b × 1.03) × (1 + 0.04) = b × 1.03 × 1.04 = b × (1.03 × 1.04) = b × 1.0712 We need to find overall percentage price increase in the last 2 years Thus, Overall percentage increase = (𝑂𝑣𝑒𝑟𝑎𝑙𝑙 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑝𝑟𝑖𝑐𝑒)/(𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑝𝑟𝑖𝑐𝑒) × 100 = (𝑷𝒓𝒊𝒄𝒆 𝒂𝒇𝒕𝒆𝒓 𝒀𝒆𝒂𝒓 𝟐 − 𝑰𝒏𝒊𝒕𝒊𝒂𝒍 𝑷𝒓𝒊𝒄𝒆)/(𝑰𝒏𝒊𝒕𝒊𝒂𝒍 𝒑𝒓𝒊𝒄𝒆) × 100 = (𝑏 × 1.0712 − 𝑏)/𝑏 × 100 = (𝑏 × 0.0712)/𝑏 × 100 = 0.0712 × 100 = 00712/10000 × 100 = 712/10000 × 100 = 712/100 = 7.12% Thus, the total increase is 7.12%. (It is NOT 3 + 4 = 7%)