Example 3 (Page 16) - Chapter 1 Class 8 - Fractions in Disguise (Ganita Prakash II)

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Example 3 (Page 16) Do the following two statements mean the same thing? (i) The population of this state in 1991 is 165% of that in 1961. (ii) The population of this state has increased by 65% from 1961 to 1991.The questions asks if these two sentences mean the same thing: Population is 165% of the old population. Population increased by 65% from the old population. Let's test it with a number! Imagine the population in 1961 was 100 people. Scenario A (is 165%) It says, the population of this state in 1991 is 165% of that in 1961 So, Population in 1991 = 165% of Population in 1961 = 165% × Population in 1961 = 165/100 × 100 = 165 people Scenario B (increased by 65%) It says, The population of this state has increased by 65% from 1961 to 1991 So, Population in 1991 = Population in 1961 + 65% of Population in 1961 = Population in 1961 + 65% × Population in 1961 = 100 + 65/100 × 100 = 100 + 65 = 165 Thus, both values are the same So, we can conclude Saying "I have 165% of what you have" is the same as saying "I have what you have, plus 65% more." So, Population in 1991 = 165% of Population in 1961 = 165% × Population in 1961 = 165/100 × 100 = 165 people Scenario B (increased by 65%) It says, The population of this state has increased by 65% from 1961 to 1991 So, Population in 1991 = Population in 1961 + 65% of Population in 1961 = Population in 1961 + 65% × Population in 1961 = 100 + 65/100 × 100 = 100 + 65 = 165 Thus, both values are the same So, we can conclude Saying "I have 165% of what you have" is the same as saying "I have what you have, plus 65% more."